Find the matrix with respect to the standard basis vectors for the linear transformation that rotates every vector in through an angle of and then reflects it across the -axis.
A linear transformation is formed by reflecting every vector in in the -axis and then rotating the resulting vector through an angle of . Find the matrix of this linear transformation.
A vector in is rotated counterclockwise about the origin through an angle of , and the result is reflected in the -axis. Find, with respect to the standard basis, the matrix of this combined transformation.