Fix a real number θ and define the transition matrix from the standard ordered basis S on...

Fix a real number θ and define the transition matrix from the standard ordered basis S on ℝ2 to a second ordered basis B by

a. If  then find [v]B.

b. Draw the rectangle in the plane with vertices

c. Let . Draw the rectangle in the plane with vertices the coordinates of the vectors, given in part (b), relative to the ordered basis B.