The first one emphasises recency or continuing relevance to the present situation. The radio must still be off.
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rpshStill be off! Got it! Thank you so much!It could still be off in the case of "Why did you turn off the radio?", of course. However, "Why did you turn off the radio?" can be used about historical events that have no relevance to the current state of the radio, while "Why have you turned off the radio?" cannot.