You work in the company „HHN Mechatronics & Robotics“ and are supposed to generate a bipolar signal ($-10V ... + 10V$) from a unipolar signal of a digital-to-analog converter ($0...5V$) in a project. A colleague recommended the circuit shown on the right.

1. First, analyze what change is made by pressing the switch $S$. How does the output signal change?
2. Try to mathematically determine the relationship of $U_A$ and $U_E$ as $U_A(U_E)$ by superposition.
3. The circuit still has the problem that the positive half-wave is output negatively. What further circuit must be provided after this so that this problem can be solved?