The correct answer to this question is the following.
The power that allows the president to take each action is:
Sign a nuclear weapons agreement with Russia: Making treaties.
Send the Army Corps of Engineers to a disaster area: Command the Military.
Select a new Supreme Court Justice: Appointing Ambassadors and justices.
The President of the United States is a powerful person and the US Constitution grants its powers and faculties to do its work as the most important figure in the United States. The US President is the Chief Diplomat of the country. He also is the Commander-in-Chief of the armed forces. He has the veto power in case he doesn't approve laws sent by Congress. The President can also appoint judges to the Supre Court, and appoint Ambassadors.