Challenge question: Logarithmic spiral

In this question we are going to use some simple matrix transformations to create some fun plots.

A point $p=(x,y)$ in two space can be represented as a column vector, i$.$e$.$ a $21$ matrix

$p=\left[\begin{array}{c}x\\ y\end{array}\right]$

Such a point can be rotated counter clockwise $$ radians about the origin by multiplying on the left by the matrix:

$\left[\begin{array}{cc}cos()& -sin()\\ sin()& cos()\end{array}\right]$

For example we could represent the rotation of the point $p=(1,2)$ by $\frac{}{2}(90)$ counter clockwise as:

$\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]\left[\begin{array}{c}1\\ 2\end{array}\right]=\left[\begin{array}{c}-2\\ 1\end{array}\right]$

Furthermore, a point can be scaled by $s$ with respect to the origin by multiplying on the left by the matrix

$\left[\begin{array}{cc}s& 0\\ 0& s\end{array}\right]$

Notes:

You are allowed to use loops and comprehensions.

The above plot was made with the call plot$\_$log$\_$spiral$(505,5,1.$e$1)$

The title should be the same as in the plot above, i$.$e$.$ of the form "Logarithmic Spiral: $n=\{n\},$ rotation $=\{$theta in radians to $2$ decimal places