1.When the plane is rotated 45degree about the point (2,-1), then what would be the image of the point (4<3)?
well, the rotation matrix R is
(cosθ sinθ)
(-sinθ cosθ)
Since (4,3)-(2,-1) = (2,4)
(2,4)*R = (-√2,3√2)
Add that back to the original point, and you have (2-√2 , -1+3√2)