Why would an airliner make a 90° course change?
This answer assumes the manouevring was related to the Military training activities going on off-shore. While plausible, there is another plausible explanition in ymb1's answer.



That was a British Airways Boeing 747 on its way from London to Miami.

Just off the coast there is a military exercise going on (see the LJ35 doing circles in the screenshot from flightradar24.com below; probably a military contractor like the one in this question).

Therefore all flights that would normally fly in that area end up flying over the coast. It seems that when the peak traffic from Europe towards Miami was passing, ATC decided to put everybody onto their original route as soon as they passed the bottleneck in order to reduce the traffic density. The result is quite a few sharp turns.



A few hours later there were at least 4 Learjets playing around off the coast. Note that most military traffic is not shown on FR24, so it may have been quite a bit busier.