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-361 Easiteach 2 45 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 18 301 323 -301 -330 0 yyyyyd Outline 321 -315 303 -316 11 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 289 317 -314 -427 0 yyyyyd Outline 303 -316 303 -425 12 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 33 709 731 -329 -356 0 nyyyyd Outline 62 0 46 n 0 n 16777216 0 0 0 0 0  43 5 00000005 43 2 00000079 43 1 00000000 15 701 765 -356 -438 0 yyyyyd 707 -417 Easiteach 2 43 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 33 711 733 -385 -412 0 nyyyyd Outline 62 0 44 n 0 n 16777216 0 0 0 0 0 rqqqqqqqqqqqqqqqqqqq 43 5 00000005 43 2 00000079 43 1 00000000 18 289 317 -411 -439 0 yyyyyd Outline 303 -425 303 -425 13 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 301 321 -411 -439 0 yyyyyd Outline 303 -425 319 -425 14 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 583 605 -303 -332 0 yyyyyc Outline 603 -317 585 -318 15 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 571 599 -316 -429 0 yyyyyc Outline 585 -318 585 -427 16 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 571 599 -413 -441 0 yyyyyc Outline 585 -427 585 -427 17 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 583 603 -413 -441 0 yyyyyc Outline 585 -427 601 -427 18 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 922 942 -302 -331 0 yyyyyb Outline 940 -316 924 -317 19 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 926 954 -302 -330 0 yyyyyb Outline 940 -316 940 -316 20 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 926 955 -314 -427 0 yyyyyb Outline 941 -425 940 -316 21 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 477 576 -348 -385 0 yyyyyb Outline 481 -365 572 -367 22 n 0 n 0 0 0 24 6 00000001 24 5 00000005 24 2 00000079 18 921 943 -411 -441 0 yyyyyb Outline 923 -427 941 -425 23 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 414 434 -303 -332 0 yyyyya Outline 432 -317 416 -318 24 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 418 446 -303 -331 0 yyyyya Outline 432 -317 432 -317 25 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 418 447 -315 -428 0 yyyyya Outline 433 -426 432 -317 26 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 413 435 -412 -442 0 yyyyya Outline 415 -428 433 -426 27 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 15 179 1079 -83 -165 0 yyyyy` 185 -144 Easiteach 37 28 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 If we put our results together we get 16 0 352800 37 55 -15 0 1 0 23 5 0 000004D8 15 612 706 -294 -436 0 yyyyy` 618 -355 Easiteach 7 38 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 cos sin 16 0 30400 3 55 -15 0 1 0 16 4 25600 3 55 -15 0 1 0 23 18 0 00000079 23 5 0 00000343 18 539 760 -433 -626 0 yyyyy` Outline 559 -606 740 -453 49 n 0 n 0 0 0 24 6 00000001 24 5 00000014 24 2 00000079 24 0 4888ff00 15 275 1279 -633 -775 0 yyyyy` 281 -694 Easiteach 83 54 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 This is our transformation matrix for any rotation anti-clockwise about the origin. 16 0 394400 41 55 -15 0 1 0 16 42 374000 41 55 -15 0 0 0 23 4 0 FF702800 23 5 0 0000048A 23 4 51 3800A800 19 620 919 -312 -428 0 yyyyy_ Outline 57 n 0 n 0 0 0 0 0 0 620 -428 919 -312 24 5 00000005 24 2 00000079 24 1 ffd7eb00 15 319 429 -358 -440 0 yyyay_ 325 -419 Easiteach 4 4 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 1 16 0 36800 4 55 -15 0 1 0 23 5 0 00000425 60 53 0 0 61 45 61 46 60 52 0 0 61 43 61 44 60 51 0 0 61 24 61 25 61 26 61 27 60 50 0 0 61 19 61 20 61 21 61 23 60 49 0 0 61 15 61 16 61 17 61 18 60 48 0 0 61 11 61 12 61 13 61 14 60 47 0 0 61 9 61 10 60 46 0 0 61 7 61 8 13 0 -1150 1488 0 J:\Lessons\A-Level\Further_maths\Further_Pure_1\Matrices\Transformations\Rotations.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 2 0 0 -1 -1 -1 0 65536  0 0 0 0 2 0 1557 0 0 0 0 0 6 0 1 0 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 ETRotate 0 0 FF000000 00FF0000 nyn 00 0 yn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 18 106 151 -141 -759 0 yyyyyg Outline 129 -749 128 -151 1 n 0 n 0 0 0 24 6 00000001 24 5 0000000a 24 2 00000079 18 36 735 -656 -701 0 yyyyyg Outline 46 -679 725 -678 2 n 0 n 0 0 0 24 6 00000001 24 5 0000000a 24 2 00000079 18 126 444 -347 -681 0 yyyyyf Outline 131 -676 439 -352 3 n 0 n 0 0 0 24 5 0000000a 24 2 00000079 24 0 3800a800 18 422 453 -354 -681 0 yyyyyf Outline 436 -356 439 -679 4 n 0 n 0 0 0 24 2 00000079 24 0 d070ff00 24 5 00000005 18 124 552 -662 -697 0 yyyyyf Outline 129 -680 547 -679 5 n 0 n 0 0 0 24 5 0000000a 24 2 00000079 24 0 3800a800 33 421 448 -338 -371 0 nyyyye Outline 88 0 6 n 0 n 0 0 0 0 0 0  43 0 0000ff00 43 5 0000000a 33 424 443 -339 -378 0 nyyyye Outline 106 0 7 n 0 n 0 0 0 0 0 0  43 0 0000ff00 43 5 0000000a 33 535 552 -666 -690 0 nyyyye Outline 61 0 8 n 0 n 0 0 0 0 0 0 c`__^]\Z Y X!V"V#V#U$U$T$S$R%R%Q 43 0 0000ff00 43 5 0000000a 33 533 550 -663 -696 0 nyyyyd Outline 88 0 9 n 0 n 0 0 0 0 0 0 KKKKMNNOQRSTUVX Y Z \ ] ^!_!`!a"a"c"d#d#e#f 43 0 0000ff00 43 5 0000000a 15 484 673 -729 -811 0 yyyyyd 490 -790 Easiteach 7 10 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 M (1,0) 16 0 68400 7 55 -15 0 1 0 23 5 0 00000316 23 4 0 FF702800 15 473 555 -295 -377 0 yyyyyc 479 -356 Easiteach 2 11 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 M' 16 0 25600 2 55 -15 0 1 0 23 5 0 00000321 23 4 0 FF702800 33 203 234 -618 -676 0 nyyyyc Outline 169 0 12 n 0 n 0 0 0 0 0 0 `__`acdefhhjklmopqqrsuvwwz{|}~~ 43 5 0000000a 33 203 234 -605 -636 0 nyyyyb Outline 67 0 13 n 0 n 0 0 0 0 0 0  43 5 0000000a 33 189 219 -618 -644 0 nyyyyb Outline 49 0 14 n 0 n 0 0 0 0 0 0  43 5 0000000a 15 225 274 -416 -498 0 yyyyya 231 -477 Easiteach 1 15 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1 16 0 12400 1 55 -15 0 1 0 23 5 0 00000419 23 4 0 FF702800 15 276 320 -677 -759 0 yyyyya 282 -738 Easiteach 1 16 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 a 16 0 10400 1 55 -15 0 1 0 23 5 0 000003E6 15 457 505 -460 -542 0 yyyyy` 463 -521 Easiteach 1 17 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 b 16 0 12000 1 55 -15 0 1 0 23 5 0 00000331 15 166 215 -610 -692 0 yyyyy` 172 -671 Easiteach 1 18 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 12400 1 55 -15 0 1 0 23 4 0 FF702800 23 5 0 000004B4 33 175 197 -636 -667 0 nyyyy` Outline 52 0 19 n 0 n 16777216 0 0 0 0 0  dt s ssssɶsssssxsks]sOs5s's 43 0 ff702800 43 7 00000005 43 5 0000000a 15 835 940 -203 -285 0 yyyay_ 841 -264 Easiteach 4 20 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 = 16 0 34800 4 55 -15 0 1 0 23 5 0 000004B4 15 755 864 -196 -278 0 yyyyy^ 761 -257 Easiteach 4 21 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 cos 16 0 36400 4 55 -15 0 1 0 23 5 0 0000028F 23 18 0 00000079 33 843 866 -230 -262 0 nyyyy^ Outline 52 0 22 n 0 n 16777216 0 0 0 0 0 N N N O Q R S T U V X Y Z [ \ ] _ 43 5 0000000a 15 926 970 -173 -255 0 yyyyy] 932 -234 Easiteach 1 23 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 a 16 0 10400 1 55 -15 0 1 0 23 5 0 000001B7 18 920 973 -229 -257 0 yyyyy] Outline 922 -243 971 -243 24 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 15 931 980 -233 -315 0 yyyay] 937 -294 Easiteach 1 25 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1 16 0 12400 1 55 -15 0 1 0 23 5 0 000001AA 15 1105 1281 -203 -285 0 yyyyy\ 1111 -264 Easiteach 7 26 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 a = cos 16 0 63200 7 55 -15 0 1 0 23 5 0 0000014C 23 18 4 00000079 15 1269 1333 -206 -288 0 yyyay\ 1275 -267 Easiteach 2 27 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000004B4 33 1277 1300 -233 -265 0 nyyyy\ Outline 52 0 28 n 0 n 16777216 0 0 0 0 0      43 5 0000000a 15 766 863 -426 -508 0 yyyyy\ 772 -487 Easiteach 4 29 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 sin 16 0 31600 4 55 -15 0 1 0 23 5 0 0000028F 15 846 951 -433 -515 0 yyyay\ 852 -494 Easiteach 4 30 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 = 16 0 34800 4 55 -15 0 1 0 23 5 0 000004B4 15 937 985 -403 -485 0 yyyyy[ 943 -464 Easiteach 1 31 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 b 16 0 12000 1 55 -15 0 1 0 23 5 0 000001B7 15 1116 1284 -433 -515 0 yyyyy[ 1122 -494 Easiteach 7 32 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 b = sin 16 0 60000 7 55 -15 0 1 0 23 5 0 0000014C 18 931 984 -459 -487 0 yyyyy[ Outline 933 -473 982 -473 33 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 33 854 877 -460 -492 0 nyyyy[ Outline 52 0 34 n 0 n 16777216 0 0 0 0 0 Y%Y#Y#Z#\#]#^#_#`#a#c#d#e#f#g#h#j# 43 5 0000000a 15 942 991 -463 -545 0 yyyay[ 948 -524 Easiteach 1 35 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1 16 0 12400 1 55 -15 0 1 0 23 5 0 000001AA 15 1280 1344 -436 -518 0 yyyayZ 1286 -497 Easiteach 2 36 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000004B4 33 1288 1311 -463 -495 0 nyyyyZ Outline 52 0 37 n 0 n 16777216 0 0 0 0 0  "                   43 5 0000000a 15 80 816 -822 -904 0 yyyyyZ 86 -883 Easiteach 35 40 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Image of (1,0) is (cos , sin ) 16 0 287200 35 55 -15 0 1 0 23 4 0 FF28B800 23 5 0 0000054D 23 18 19 00000079 15 585 649 -827 -909 0 yyyyyZ 591 -888 Easiteach 2 42 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 4 0 FF28B800 23 5 0 000002C0 33 595 617 -856 -883 0 nyyyyZ Outline 61 0 45 n 0 n 16777216 0 0 0 0 0 TTUUVWXZ[\^_`abcefgh 43 0 ff28b800 43 5 00000005 15 726 790 -826 -908 0 yyyyyY 732 -887 Easiteach 2 51 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 23 4 0 FF28B800 33 736 758 -855 -882 0 nyyyyY Outline 61 0 50 n 0 n 16777216 0 0 0 0 0  43 0 ff28b800 43 5 00000005 15 372 421 -917 -999 0 yyyyyY 378 -978 Easiteach 1 53 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1 16 0 12400 1 55 -15 0 1 0 23 5 0 00000429 15 638 702 -919 -1001 0 yyyyyY 644 -980 Easiteach 2 60 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 33 648 670 -948 -975 0 nyyyyY Outline 62 0 59 n 0 n 16777216 0 0 0 0 0 ?>>>>>>>>>>>>>>>>>>> 43 5 00000005 43 2 00000079 43 1 00000000 15 368 417 -976 -1058 0 yyyyyY 374 -1037 Easiteach 1 54 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 12400 1 55 -15 0 1 0 23 5 0 00000425 15 556 665 -916 -998 0 yyyyyX 562 -977 Easiteach 4 56 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 cos 16 0 36400 4 55 -15 0 1 0 23 18 0 00000079 23 5 0 00000371 15 563 645 -970 -1052 0 yyyyyX 569 -1031 Easiteach 3 57 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 sin 16 0 25600 3 55 -15 0 1 0 23 5 0 00000369 15 639 703 -975 -1057 0 yyyyyX 645 -1036 Easiteach 2 62 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 0 16 0 18400 2 55 -15 0 1 0 23 5 0 000002C0 33 649 671 -1004 -1031 0 nyyyyX Outline 62 0 61 n 0 n 16777216 0 0 0 0 0  43 5 00000005 43 2 00000079 43 1 00000000 18 353 375 -919 -948 0 yyyyyW Outline 373 -933 355 -934 67 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 341 369 -932 -1045 0 yyyyyW Outline 355 -934 355 -1043 68 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 341 369 -1029 -1057 0 yyyyyW Outline 355 -1043 355 -1043 69 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 353 373 -1029 -1057 0 yyyyyW Outline 355 -1043 371 -1043 70 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 549 571 -921 -950 0 yyyyyV Outline 569 -935 551 -936 77 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 537 565 -934 -1047 0 yyyyyV Outline 551 -936 551 -1045 76 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 537 565 -1031 -1059 0 yyyyyV Outline 551 -1045 551 -1045 75 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 549 569 -1031 -1059 0 yyyyyV Outline 551 -1045 567 -1045 74 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 664 684 -918 -947 0 yyyyyU Outline 682 -932 666 -933 78 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 668 696 -918 -946 0 yyyyyU Outline 682 -932 682 -932 79 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 668 697 -930 -1043 0 yyyyyU Outline 683 -1041 682 -932 80 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 663 685 -1027 -1057 0 yyyyyU Outline 665 -1043 683 -1041 81 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 399 419 -919 -948 0 yyyyyT Outline 417 -933 401 -934 82 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 403 431 -919 -947 0 yyyyyT Outline 417 -933 417 -933 83 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 403 432 -931 -1044 0 yyyyyT Outline 418 -1042 417 -933 84 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 398 420 -1028 -1058 0 yyyyyT Outline 400 -1044 418 -1042 85 n 0 n 16777216 0 0 24 5 00000005 24 2 00000079 18 443 542 -966 -1003 0 yyyyyS Outline 447 -983 538 -985 88 n 0 n 0 0 0 24 6 00000001 24 5 00000005 24 2 00000079 19 757 912 -205 -294 0 yyyyyR Outline 92 n 0 n 0 0 0 0 0 0 757 -294 912 -205 24 5 00000005 24 2 00000079 24 1 ffd7eb00 19 764 919 -432 -521 0 yyyyyR Outline 94 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffd7eb00 19 923 979 -207 -295 0 yyyyyQ Outline 95 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffd7eb00 19 933 989 -416 -526 0 yyyyyQ Outline 96 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffd7eb00 19 1092 1332 -206 -296 0 yyyyyP Outline 97 n 0 n 0 0 0 0 0 0 1092 -296 1332 -206 24 5 00000005 24 2 00000079 24 1 ffd7eb00 19 1108 1348 -436 -526 0 yyyyyP Outline 99 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffd7eb00 19 62 881 -815 -1061 0 yyyyyP Outline 100 n 0 n 0 0 0 0 0 0 62 -1061 881 -815 24 5 00000005 24 2 00000079 24 1 ffd7eb00 60 23 0 0 61 82 61 83 61 84 61 85 60 22 0 180 61 78 61 79 61 80 61 81 60 21 0 0 61 74 61 75 61 76 61 77 60 20 0 0 61 70 61 69 61 68 61 67 60 19 0 0 61 61 61 62 60 18 0 0 61 59 61 60 60 17 0 0 61 50 61 51 60 16 0 0 61 45 61 42 13 0 -1150 1488 0 J:\Lessons\A-Level\Further_maths\Further_Pure_1\Matrices\Transformations\Rotations.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 1 0 0 -1 -1 -1 0 65536  0 0 0 0 1 0 1557 0 0 0 2318 0 7 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yy 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 ETRotate 0 0 FF000000 00FF0000 nyn 00 0 yn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 25 6 :c.$.program_files.research_machines.easiteach.multimedia.toys_and_games.toys_and_games_-_general.frisbee/gif 21966 4 y 0 0 GIF89aJI&%Nos*5v)KRd֙Yx38ݮÌzh' ,I)%3͗()  l٢5#9Bʺ\giưߨgwwL߲֭/Te#oەb| 46!05ݫ3y9hmTouhUltp%Cr#)•@7n]t6֘-cL0;Zutn O"7zŠ3kA+OZ-5Vu2)ذװڶ1-u[D|CM<8zycnyuˁֱËWSG[xᾍA:gqZ r5N4ނ .SI^i&{f+ q!{&gBt`gLdUi}}DvNnaVو4wAuxH`@H`TiĕF$r1UJHIǙg-'㇕5[5%pEZ%nOo#6b+W%X L 堙 (dY]!&W[0mEo5h&u^Fd "Ɨ]"`F$`QlSH\9k|t@{}Adk vue#+5X:J"b/"؛ \*"%qf_:,Ƽ-{O^B0%!+-jion؟`dbA&hh!^@$&,$DK&< O!Ԁ<Я!eoUFeK~"cgYh:~qAUzO`*hq":p HM / 7 *!f8-p9S[} 5\r}],z|ݙ楶NMjQi 4b`iB\5M&B'3M#c:~*ğ KB S7Ɨtպ,lDB^6&AщmrQZy3~pZe XS0= x\)=}O|+_f7̀5 EY0J͉`MmkrMM؄,niSf< m8%[I@ P6 . 1`@k?f;@0A݂pҐ%bUpRv2uA TE/vD$jr8U*G CDh@\8o 7^@.t?@L \Њ4IH9_Our"_N%d#D.r_Ue{  ~n7҅%LsVd 9`2k^IP& c{nkÎFF2*(!c(<[U hF&hPC=_Wu @F-6> Hͺ>p"FRG)U91)SԦx˛)$E@I)#BGeU% e搙(p 0|H`As%30Y%'^OU;!k`(ZtJ*vFR9>r8B؆EݧG$ [s0@A 76r=@XL(ߴ(Oۚ?pw$qK#8^=A/yP21TBGm{`/ &;9 @E%9Tr0e2Ā5 k^@[X  :ѧ̻M˝# JsjIB23ۆT(b̲h0VACHAs4yĠF,bh 5m` cр HhqI?&hC6=@0`PX:eݖS'.B@Y;@C,2G>W Xw7 ڐ=WŔpPD|1 j a 8 }(:PUG/`aZ3 z4hJ 6WMAh00$~"m"t6r;GmTwt*"zrgcs0WffoEPKP GJg%RWU2 a|P 5DRq-|'p0XfssI r `G\`EIt E4b%8"b'}@hq2_T/ s ~s0>(a0pg(N=+ bs X /‹d:-C]` B 1X $$a sv̥s^rcc9ACr',4]/ iH\oe}>HaP  pgg9pT:|{b+;c:P0$)b{- `ahaG z@w\ru\Es ?/s)h)BS2nGt8HFPn&?h1 ȅ9^(p+ 5aPPESP#5d& &5ҘhE-AU21Solxapy  _-W `Y,G&)~@SK+q7aY,zn2@ HOQё$_CP'p|^@ O$0 a p+`&idi`cИ3hv//:0{`-Qqk9P PuhJ.M/ Ԡ%B<0 _ ?.f;uJjȘ L${b-p|Xۡ:F y]  Hʋ/g˜Y2PpN#2Jvj/e P @ 1}S 0+P oWX0 ˀ몡п۳:٪3/g`0|IjB y}@܈Ybҽ1<){6E8/Z2u?k(4`lwSP Gq 9pf p '+c<ƙ ̞۳<̝+4 ʗh g+w7thj=X] ` }0ȅ @8 `;.c'Ke1Y'2E"~Z2U hD4 @\yPP}g@X PBs0 {Pتhx'Ѡf{˷%j4j Mky,}@\KŽ`(\" Qza7w-j"PQe:~! /1H2Y5x 9 @pS%oS_P 0 =h$̅& TFRS8s  `|WzkI  ` Em }y3f+B"Nv-b<pMAM_D^2| s2}ںËS,"XjXv# Π BƖ!Cpyp_0q xhwOVXL`YNBU>ߌخؿl;51>ëWؙ2 7p PpN ΃ H+ ~b! 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