The vector $\vec{A}$ (red) has length $8$, and makes an angle of $3\pi/19$ with the $x$-axis. The vector $\vec{B}$ (blue) has length $6$, and makes an angle of $8\pi/19$ with the $x$-axis.

Find the matrix which rotates and dilates vector $A$ into vector $B$:

$\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

$\left\lbrack\begin{array}{r} 8 \cos(3\pi/19) \\ 8 \sin(3\pi/19) \end{array}\right\rbrack = \left\lbrack\begin{array}{r} 6 \cos(8\pi/19) \\ 6 \sin(8\pi/19) \end{array}\right\rbrack$