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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!

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!

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