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## Homework Statement

The vector A has length 8.5, and makes an angle of 5pi/19 with the x-axis.

The vector B has length 6, and makes an angle of 8pi/19 with the x-axis.

Find the matrix which rotates and dilates vector into vector .

## Homework Equations

Rotation matrix in counterclockwise direction: \begin{equation}

\left[

\begin{array}{ccc}

cos∅ & -sin∅\\

sin∅ & cos∅\\

\end{array}

\right]

\end{equation}

Dilation matrix:

\begin{equation}

\left[

\begin{array}{ccc}

c & 0\\

0 & c\\

\end{array}

\right]

\end{equation}

## The Attempt at a Solution

\begin{equation}

\left[

\begin{array}{ccc}

(12/17)cos(3pi/19) & -sin(3pi/19)\\

sin(3pi/19) & (12/17)cos(3pi/19)\\

\end{array}

\right]

\end{equation}

My line of thinking: to move A into B, it needs to move counterclockwise from its current positions by an angle of 3pi/19. A needs to "shrink" by a factor of 12/17.

However, this is incorrect. I would really appreciate it if someone could point me in the right direction, or even give me a similar example. Thank you.