Let $\displaystyle T: \Re^2 \rightarrow \Re^2 $ be the map that first projects points on to the line $\displaystyle x_2=\sqrt {3}x_1 $ than rotates 30 degrees clockwise.

a) Find the matrix representation of T.

b) Find the range of T (describe it).

c) Find the nullset of T (describe it).

Sorry for posting so many problems. I'm new to this subject and I'm confused.

Thank you!