The letter F shown below is rotated $90^\circ$ clockwise around the origin, then reflected in the $y$-axis, and then rotated a half turn around the origin. What is the final image?
[Foriginal.png](https://artofproblemsolving.com/wiki/index.php/File:Foriginal.png)
[Fproblem.png](https://artofproblemsolving.com/wiki/index.php/File:Fproblem.png)
The first rotation moves the base of the $F$ to the negative $y$-axis, and the stem to the positive $x$-axis. The reflection then moves the stem to the negative $x$-axis, with the base unchanged. Then the half turn moves the stem to the positive $x$ axis and the base to the positive $y$-axis, choice $\boxed{\mathbf{(E)}}$.