June 13th, 2013, 08:08 PM  #1 
Newbie Joined: Mar 2012 Posts: 21 Thanks: 0  Problem with matrices.
Hi, hi! I'd like you help with the two following problems: (a) Verify that the 2 x 2 matrix is an orthogonal matrix. (b) Let T be the linear transformation with the above matrix A relative to the usual basis {i,i}. Prove that T maps each point in the plane with polar coordinates onto the point with polar coordinates . Thus, T is a rotation of the plane about the origin, 0 being the angle of rotation. I don't have any problem with a). But I not sure how to prove the second. ¿How do I prove the relation of a transformation with its geometric interpretation? 
June 16th, 2013, 12:03 PM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Problem with matrices.
The point with polar coordinates has Cartesian coordinate . Multiply that by the given matrix. You will need the trig identities and .


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