- #1

DDrew

- 1

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## Homework Statement

Find the points fixed by f, and show it is a

__line__. We know that f is an isometry.

0 [tex]\leq[/tex] [tex]\theta[/tex] < 2[tex]\Pi[/tex]

f: R[tex]^{2}[/tex] [tex]\rightarrow[/tex] R[tex]^{2}[/tex]

f(x) = Ax

A = | cos [tex]\theta[/tex] sin [tex]\theta[/tex] |

...| sin [tex]\theta[/tex] -cos [tex]\theta[/tex]|

## Homework Equations

fix(f) = {x | f(x) = x}

## The Attempt at a Solution

fix(f) = | (x1)(cos [tex]\theta[/tex]) + (x2)(sin [tex]\theta[/tex]) = x1 |

...| (x1)(sin [tex]\theta[/tex]) + (x2)(cos [tex]\theta[/tex]) = x2 |

The thing that confuses me the most is rotating about a line in R[tex]^{2}[/tex]. I was under the impression you could only rotate around a point? Is there something I'm missing? I'm not looking for the answer so much as I'm looking to be pointed in the right direction.

I apologize for my messy matrix formatting.