1 Suppose
Explain why this is a rotation matrix and find the angle of rotation.
2 Let T be the linear map that reflects a vector v in R2 about the line y = mx.
Use a change of basis argument to find the matrix representation A for T.
3 Let
.
Show that Q is orthogonal with determinant −1. Find the axis of rotation, the plane of reflection and the cosine of the angle of rotation.
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