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 R 2 about the...

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.