You are correct, it is genitive plural. The nominative singular form is градус.
You can easily find this yourself, actually. There are any number of sites available, but I like this one: http://www.morfologija.ru/%D1%81%D0%BB%D0%BE%D0%B2%D0%BE%D1%84%D0%BE%D1%80%D0%BC%D0%B0/%D0%B3%D1%80%D0%B0%D0%B4%D1%83%D1%81%D0%BE%D0%B2
The word "minus" has a number of different grammatical functions in English:
"The word minus is a conjunction when used as a mathematical term for the difference between two numbers.
"It can also be a preposition, and adjective and a noun." https://www.answers.com/Q/What_part_of_speech_is_minus
Here I think it's an adjective modifying "twenty degrees". It's not a mathematical function. Or maybe it's a preposition. It's not a noun here. (Example of noun: "Lying to the FBI is a real minus for your future plans.")
Three times I had the chance to watch friends who were seeing snow for the first time or experiencing minus temperatures for the first time. It was a pleasure to watch them and to see and hear the reactions. Two girls who saw it snowing for the first time were dancing around and catching snow flakes and one said: "I thought it was like a refrigerator. But this is soooo much better than a refrigerator!" :o)
This translation contains an imperfection.
Even though commonly accepted, using "minus" with temperature is actually wrong. "Minus" implies a mathematical operation, i.e. 2 - 1 two MINUS one In this case the number is negative so we should use either "negative" or "below", i.e. Negative twenty degrees or Twenty below (zero).
@ipattorneyliza: Yes, you are right and in fact I wrote: "Even though commonly accepted..." .
I don't want to draw a line between what is correct and what is commonly used. I just feel that we should give a priority to what is correct. Therefore I would keep "minus twenty degrees" as an accepted translation for this sentence but having Duolingo not accepting my "Negative twenty" while displaying "minus twenty" as the correct entry feels completely wrong to me.
Let me make out an example: How would you feel if you translated "Где ты" into "Where are you" and Duolingo did not accept it while it displayed "where are you at" as the correct translation?
As this is a Russian course and not an English one, I would accept both but display only "Where are you" as the correct entry.
I hope I was able to convey my emotions. I feel like a grammar nazi now. LOL
p.s. I believe educated people in the US tend to say "Negative".
My husband and I are American, and educated. We both have degrees in the sciences -- he has a PhD in materials science and I have a chemistry degere and a JD. We both use "minus 20," as do most everyone we know. At some point, colloquial language becomes standard and correct language, and that point arrived long ago for this expression. In fact, we now live in the UK, and today I heard someone on the train use the "minus" expression for temperature. It was also used on Euronews today by someone speaking German. So it cannot be as bad as all that!
You are correct. I would venture to say that common usage depends a lot on which part of America or which English-speaking country you're from. For example, people from Chicago (my home city) talk very differently than people in Brooklyn, NY, and both dialects differ drastically from Cockney slang :)
I entirely agree with everything you say, though I didn't actually realise the technical difference between "minus" and "negative". Have a lingot for teaching me something new today!
That said, in British English, "negative two etc" is rarely used in general day-to-day speech and actually sounds very American to my ear (at least from my POV!).