Final answer:
Two locations with zero-Doppler wind speed in a rotating wind pattern would be detected by a Doppler radar when its beam is aiming directly East or West, as the actual wind at these points blows perpendicular to the radar's beam.
Step-by-step explanation:
Doppler radar is a tool that measures the radial velocity of objects by detecting changes in the frequency of the waves that are reflected back to the radar. This effect of frequency change is known as the Doppler effect. In the scenario where the wind velocity needs to be measured, the Doppler radar can only detect movement toward or away from the radar, not perpendicular movements. For locations within a rotating wind pattern where no motion is detected, the actual wind direction must be perpendicular to the radar beam's path. Given that the radar beam is in the east-west orientation, these locations of zero Doppler wind speed would be detected when the radar is aiming directly east or west, as the motion of the winds is northwards or southwards, hence perpendicular to the radar beam.
Using this information, the correct answers to denote these points of zero-Doppler wind speed are when the radar beam is in the East and West positions.