## Maps in the plane

Determine matrices of the following linear maps in the plane ($$\mathbb R^2\to \mathbb R^2$$) with respect to the canonical base $$K$$.

• #### Variant 1

the axis symmetry w.r.t. to axis of the 1st and the 3rd quadrant.

• #### Variant 2

counterclockwise rotation by $$90^\circ$$ around the origin (the first axis is vertical, the second horizontal).

• #### Variant 3

counterclockwise rotation by $$\alpha$$ around the origin.

• #### Variant 4

the projection to the first coordinate $$p_1:(x,y)\to(x,0)$$