document.write( "Question 1180298: Which matrix represents the rotation of the vector (1,4) by 2pi/3 radians?\r
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Algebra.Com's Answer #809984 by Edwin McCravy(20064)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Instead of doing your problem for you, I'll do one exactly like it with\r\n" );
document.write( "different numbers.
Which matrix represents the rotation of the vector (1,5) by 3pi/5 radians?
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document.write( "We draw the given vector:\r\n" );
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document.write( "We calculate the length (magnitude) of the original vector by the\r\n" );
document.write( "Pythagorean theorem:\r\n" );
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document.write( "\"sqrt%281%5E2%2B5%5E2%29=sqrt%281%2B25%29=sqrt%2826%29=5.099019514\"\r\n" );
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document.write( "That'll also be the magnitude of the vector after we've rotate it. \r\n" );
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document.write( "The angle that the original vector makes with the x-axis has tangent 5/1 or 5\r\n" );
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document.write( "Make sure your calculator is in radian mode, find\r\n" );
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document.write( "tan-1(5) = 1.373400767 radians\r\n" );
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document.write( "next we add \"%283pi%29%2F5=1.884955592\" to that and get 3.258356359, which\r\n" );
document.write( "is the direction angle of the rotated vector.\r\n" );
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document.write( "We sketch in the rotated vector:\r\n" );
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document.write( "We find the horizontal component of the rotated vector by multiplying\r\n" );
document.write( "its magnitude by the cosine of its angle.\r\n" );
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document.write( "We find the vertical component of the rotated vector by multiplying\r\n" );
document.write( "its magnitude by the sine of its angle.\r\n" );
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document.write( "Answer, rounded off:\r\n" );
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document.write( "[-5.06,-0.59]\r\n" );
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document.write( "Now do yours exactly the same way.\r\n" );
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document.write( "Edwin
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