Which one of the following figures P, Q, R, or S, correctly shows the 45° clockwise-rotated version of figure (I)?

The correct figure is R.

To determine the correct 45° clockwise-rotated version of Figure (I), we can analyze the orientation of its main geometric components:
1. Horizontal Elements: In Figure (I), there is a prominent thick horizontal bar near the bottom and smaller horizontal connectors. Under a 45° clockwise rotation, these horizontal lines (initially at 0°) will tilt to -45°, pointing from the top-left to the bottom-right (slope of -1).
2. Vertical Elements: In Figure (I), there are three main vertical columns. Under a 45° clockwise rotation, these vertical lines (initially at 90°) will tilt to 45°, pointing from the top-right to the bottom-left (slope of 1).

We can mathematically describe the transformation of any coordinate $(x,y)$ rotated clockwise by an angle $\theta$ using the rotation equations:
$x^{\prime }=x\cos \left(\theta \right)+y\sin \left(\theta \right)$
$y^{\prime }=-x\sin \left(\theta \right)+y\cos \left(\theta \right)$
Substituting $\theta ={45}^{\circ }$ gives:
$x^{\prime }=\frac{x+y}{\sqrt{2}}$
$y^{\prime }=\frac{-x+y}{\sqrt{2}}$

By comparing the options:
- Figure R correctly matches this transformation: the long, thick bar near the bottom of Figure (I) is oriented diagonally from top-left to bottom-right, and the three columns are oriented diagonally from top-right to bottom-left.
- The other candidates (P, Q, and S) represent incorrect rotations, reflections, or misalignments of the individual components.
- Therefore, Figure R is the correct 45° clockwise-rotated version of Figure (I).