Question regarding multiple steps in linear mapping

[blhhblah]

Hi, I'm having some difficulty with this problem. I need to project a point in R² to the line x₂ = x₁ (sqrt(3)) and then rotate it 30 degrees clockwise.

I believe the 2x2 matrix to map it is just

sqrt(3) 0
0 1

and to rotate a vector clockwise as opposed to counter clockwise I think is

cosx sinx
-sinx cosx

I could be wrong about these 2 matrices. Is there anyway to merge the two? Do I multiply them? Thanks.

 

[HallsofIvy]

Yes, you "merge" two matrices by multiplying them. Be sure to multiply in the right order.