Thanks for your replies.
I took it back to the place where I got the tire rotation. After a test drive of 5 miles, the noise happened as soon as we came back to the shop. It appeared that it was coming from the back of the car somewhere. He said that he never heard a howling noise just like that. The closest was is he heard something close to that, there was a problem with a differential, but that noise was constant at all speeds no matter what you did. My sound goes away as soon as hit the brake. A young Tech spent over an hour taking both rear wheel brake assemblies a part.
The only thing out of the ordinary was that the passenger rear rotor would not come off by hand. He had to heat it up with a blow torch. It finally came off nicely after that. After taking both rotors off, there was nothing that appeared to cause a noise with the naked eye.
The only thing that he noticed is that one of the two rubber transmission mounts was cracked near the engine up front and with a crow bar he was able to lift the differential. Probably not the cause of the noise, but something that needs to be fixed.
It did not make the noise on the way home, so I am hoping that just taking the rotors off and putting them back on will re-situate them correctly. Don't know. Time will tell.