Hi,

I have a question that I don't know where to start on!

First, some necessary background info:

r denotes reflection about the x-axis.

t_a denotes translation by a vector a.

p_{theta} denotes rotation by an angle $\theta$ about the origin.

Let $s$ be the rotation of the plane with angle $\pi/2$ about the point $(1,1)^t$.

1. Write the formula for $s$ as a product $t_a*p_{\theta}$.

2. Let s denote reflection of the plane about the vertical axis $x=1$. Find an isometry $g$ such that $grg^{-1}=s$, and write s in the form $t_a*p_{\theta}*r$.

Thanks in advance for any help!