In a compass every direction is rotated to $135$ degrees from the original direction. In which direction will South-West be if the rotation took towards clockwise direction?

Let's represent standard directions by their angular positions from North ($0^{\circ }$) moving clockwise:
* $\text{North}=0^{\circ }\text{ or }360^{\circ }$
* $\text{North-East}=45^{\circ }$
* $\text{East}=90^{\circ }$
* $\text{South-East}=135^{\circ }$
* $\text{South}=180^{\circ }$
* $\text{South-West}=225^{\circ }$
* $\text{West}=270^{\circ }$
* $\text{North-West}=315^{\circ }$

Given that every direction is rotated $135^{\circ }$ in the clockwise direction:
We add $135^{\circ }$ to the original angle of South-West ($225^{\circ }$):

$$\text{New Direction Angle}=225^{\circ }+135^{\circ }=360^{\circ }$$

An angular position of $360^{\circ }$ corresponds exactly to North. Thus, the South-West direction will point to the North.