Linear transformation across a line

[1up20x6]

Using linear transformation reflection to find rotation

Homework Statement

Let T1 be the reflection about the line −4x−1y=0 and T2 be the reflection about the line 4x−5y=0 in the euclidean plane.

The standard matrix of T1 \circ T2 is what?

Thus T1 \circ T2 is a counterclockwise rotation about the origin by an angle of how many radians?

Homework Equations

\frac{1}{1+m^2}\begin{pmatrix}<br /> 1-m^2 &amp; 2m\\<br /> 2m &amp; m^2-1<br /> \end{pmatrix}

The Attempt at a Solution

I've used the relevant equation above and found that T1 \circ T2 = \begin{pmatrix}<br /> \frac{-455}{697} &amp; \frac{-528}{697}\\<br /> \frac{-455}{697} &amp; \frac{-455}{697}\end{pmatrix} and had this verified, but I have no idea how to relate this into an amount of radians rotated.

 

[tiny-tim]

hi 1up20x6!

should be \begin{pmatrix}<br /> \cos &amp; \sin\\<br /> -\sin &amp; \cos\end{pmatrix}