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"Time s" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Output Labels" -1 29 "Ti mes" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Heading" -1 26 "Ti mes" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Normal" -1 30 "Ti mes" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Comment" -1 18 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Maple Name" -1 35 "Times" 1 12 104 64 92 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Dictionary Hyp erlink" -1 45 "Times" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "He lp Emphasized" -1 22 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 40 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "LaTeX" -1 32 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Help Menus" -1 36 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Italic Small202204" -1 206 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Italic" -1 43 "Times" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small201203" -1 207 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold" -1 5 " Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "with(LinearAlgebra): \nwith(plottools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "house := polygon([[3,3],[0,3],[0,0],[3,0]], color=yellow, thickness=1);\n" }{MPLTEXT 1 0 69 "roof := polygon([[3,3],[1.5,4],[0,3]], color=yellow , thickness=1);\n" }{MPLTEXT 1 0 77 "chimney := polygon([[3,0],[3.1,0] ,[3.1,4],[3,4]], color=pink, thickness=1);\n" }{MPLTEXT 1 0 18 "t := - 90*2*Pi/360;" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 52 "M := Matrix([[cos (t), -sin(t)],[sin(t), cos(t)]]);\n" }{MPLTEXT 1 0 44 "a:=M[1,1]:b:=M[ 1,2]:d:=M[2,1]:e:=M[2,2];\n\n" }{MPLTEXT 1 0 31 "T1 := (x, y) -> (x-1. 5, y-4);\n" }{MPLTEXT 1 0 37 "T2 := (x, y) -> (a*x+b*y, d*x+e*y);\n" } {MPLTEXT 1 0 31 "T3 := (x, y) -> [x+1.5, y+4];\n" }{MPLTEXT 1 0 35 "T \+ := (x, y) -> T3(T2(T1(x, y)));\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 82 "newhouse := polygon([T(3,3), T(0,3), T(0,0), T(3,0)], color=green, thickness=1):\n" }{MPLTEXT 1 0 76 "newroof := polygon([T(3,3), T(1.5 ,4), T(0,3)], color=green, thickness=1):\n" }{MPLTEXT 1 0 86 "newchimn ey := polygon([T(3,0), T(3.1,0), T(3.1,4), T(3,4)], color=red, thickne ss=1):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "plots[display](\{house , roof, newhouse, newroof, chimney, newchimney\}, axes=normal, scaling =CONSTRAINED);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I&houseG6\"-I)POLYGON SG6$%*protectedGI(_syslibGF$6%7&7$$\"\"$\"\"!F-7$$F/F/F-7$F1F17$F-F1-I 'COLOURGF'6&I$RGBGF'$\"*++++\"!\")F8F1-I*THICKNESSGF'6#\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I%roofG6\"-I)POLYGONSG6$%*protectedGI(_ syslibGF$6%7%7$$\"\"$\"\"!F-7$$\"#:!\"\"$\"\"%F/7$$F/F/F--I'COLOURGF'6 &I$RGBGF'$\"*++++\"!\")FI(chimneyG6\"-I)POLYGONSG6$%*protectedGI(_syslibGF$6%7& 7$$\"\"$\"\"!$F/F/7$$\"#J!\"\"F07$F2$\"\"%F/7$F-F6-I'COLOURGF'6&I$RGBG F'\"\"\"$\"*w6%Hv!\"*$\"+9Vygz!#5-I*THICKNESSGF'6#F=" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"tG6\",$*&#\"\"\"\"\"#F(I#PiG%*protectedGF(!\"\"" } }{PARA 11 "" 1 "" {XPPMATH 20 ">I\"MG6\"-I'RTABLEGF$6%\"*[Bl]\"-I'MATR IXGF$6#7$7$\"\"!\"\"\"7$!\"\"F.I'MatrixG6$%*protectedGI(_syslibGF$" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I\"eG6\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#T1G6\"f*6$I\"xGF$I\"yGF$F$6$I)operatorGF$I&arrowGF$F$6 $,&F'\"\"\"$\"#:!\"\"F1,&F(F.\"\"%F1F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#T2G6\"f*6$I\"xGF$I\"yGF$F$6$I)operatorGF$I&arrowGF$F$6 $,&*&I\"aGF$\"\"\"F'F0F0*&I\"bGF$F0F(F0F0,&*&I\"dGF$F0F'F0F0*&I\"eGF$F 0F(F0F0F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#T3G6\"f*6$I\"xGF$I\" yGF$F$6$I)operatorGF$I&arrowGF$F$7$,&F'\"\"\"$\"#:!\"\"F.,&F(F.\"\"%F. F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"TG6\"f*6$I\"xGF$I\"yGF$F$6 $I)operatorGF$I&arrowGF$F$-I#T3GF$6#-I#T2GF$6#-I#T1GF$F&F$F$F$" }} {PARA 13 "" 1 "" {TEXT 208 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6% -%*AXESSTYLEG6#%'NORMALG-%)POLYGONSG6*7&7$$\"\"$\"\"!F,7$$F.F.F,7$F0F0 7$F,F07%F+7$$\"#:!\"\"$\"\"%F.F/7&F27$$\"#JF7F07$F\">THv!#<$\"1=AFNWygz!#;FhnFfnFhnFhnFfnFhnFfnFhnFhn-%(SCALINGG6#%,C ONSTRAINEDG" 1 2 2 1 10 1 2 6 1 4 1 1.0 45.0 45.0 1 0 "Curve 1" }} {TEXT 208 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "with(linal g): with(plots): with(plottools):\n" }{MPLTEXT 1 0 88 "side1 := polyg on([[-1,-1,-1],[-1,1,-1],[-1,1,1],[-1,-1,1]], color=violet,thickness=1 ):\n" }{MPLTEXT 1 0 84 "side2 := polygon([[1,-1,-1],[1,1,-1],[1,1,1],[ 1,-1,1]], color=yellow,thickness=1):\n" }{MPLTEXT 1 0 88 "side3 := pol ygon([[-1,-1,-1],[1,-1,-1],[1,-1,1],[-1,-1,1]], color=yellow,thickness =1):\n" }{MPLTEXT 1 0 84 "side4 := polygon([[-1,1,-1],[1,1,-1],[1,1,1] ,[-1,1,1]], color=yellow,thickness=1):\n" }{MPLTEXT 1 0 86 "side5 := p olygon([[-1,-1,-1],[-1,1,-1],[1,1,-1],[1,-1,-1]], color=pink,thickness =1):\n" }{MPLTEXT 1 0 84 "side6 := polygon([[-1,-1,1],[-1,1,1],[1,1,1] ,[1,-1,1]], color=yellow,thickness=1):\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 77 "M := matrix(3, 3, [1,0,0,0,sqrt(2)/2,-sqrt(2)/2, 0, s qrt(2)/2, sqrt(2)/2]):\n" }{MPLTEXT 1 0 92 "a:=M[1,1]:b:=M[1,2]:c:=M[1 ,3]:d:=M[2,1]:e:=M[2,2]:f:=M[2,3]:g:=M[3,1]:h:=M[3,2]:i:=M[3,3]:\n" } {MPLTEXT 1 0 60 "T := (x, y, z) -> [a*x+b*y+c*z, d*x+e*y+f*z, g*x+h*y+ i*z]:\n" }{MPLTEXT 1 0 93 "newside1 := polygon([T(-1,-1,-1),T(-1,1,-1) ,T(-1,1,1),T(-1,-1,1)], color=blue,thickness=1):\n" }{MPLTEXT 1 0 90 " newside2 := polygon([T(1,-1,-1),T(1,1,-1),T(1,1,1),T(1,-1,1)], color=g reen,thickness=1):\n" }{MPLTEXT 1 0 94 "newside3 := polygon([T(-1,-1,- 1),T(1,-1,-1),T(1,-1,1),T(-1,-1,1)], color=green,thickness=1):\n" } {MPLTEXT 1 0 90 "newside4 := polygon([T(-1,1,-1),T(1,1,-1),T(1,1,1),T( -1,1,1)], color=green,thickness=1):\n" }{MPLTEXT 1 0 92 "newside5 := p olygon([T(-1,-1,-1),T(-1,1,-1),T(1,1,-1),T(1,-1,-1)], color=red,thickn ess=1):\n" }{MPLTEXT 1 0 90 "newside6 := polygon([T(-1,-1,1),T(-1,1,1) ,T(1,1,1),T(1,-1,1)], color=green,thickness=1):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plots[display](\{side1, side2, side3, side4, side5, \+ \n" }{MPLTEXT 1 0 70 " newside1, newside2, newside3, ne wside4, newside5\}, \n" }{MPLTEXT 1 0 67 " axes=boxed, \+ scaling=CONSTRAINED, labels=[x, y, z]);" }}{PARA 7 "" 1 "" {TEXT 209 46 "Warning, the name GramSchmidt has been rebound" }}{PARA 7 "" 1 "" {TEXT 209 79 "Warning, the protected names norm and trace have been re defined and unprotected" }}{PARA 7 "" 1 "" {TEXT 209 49 "Warning, the \+ name changecoords has been redefined" }}{PARA 7 "" 1 "" {TEXT 209 97 " Warning, the previous binding of the name arrow has been removed and i t now has an assigned value" }}{PARA 13 "" 1 "" {TEXT 208 0 "" } {GLPLOT3D 400 400 400 {PLOTDATA 3 "6&-%*AXESSTYLEG6#%$BOXG-%+AXESLABEL SG6%Q\"x6\"Q\"yF+Q\"zF+-%)POLYGONSG6.7&7%$!\"\"\"\"!F3F37%F3$\"\"\"F5F 37%F3F7F77%F3F3F77&7%F7$F5F5$!+iN@99!\"*7%F7$\"+iN@99F@F=7%F7F=FB7%F7F >F=7&7%F3F=F>7%F3FBF=7%F3F=FB7%F3F>F=7&FGF0H$R!)4$!#<$\"27.aSHPJ%=FinFgn$F5F4$\" #5F4F\\oF\\oF\\oF]oF\\oF]oF\\oF]oF\\oF\\oF]oF]oF\\oF]oF]oF\\oF]oF]oF \\oF\\oF]oF\\oF]o$\"2gTk>\">THvFin$\"1=AFNWygz!#;-%(SCALINGG6#%,CONSTR AINEDG" 1 2 5 1 10 1 2 1 1 2 1 1.0 80.0 0.0 1 0 "Curve 1" }}{TEXT 208 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "?display" }}}{EXCHG {PARA 0 "> " 0 "" {TEXT 210 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }