Fortunately, you’ve already used the tool you need to do the job—HandBrake. Choose this MKV file as the source and then select the appropriate output preset (again I’d use Apple TV 3).

Handbrake is a wonderful open source program ... either on USB storage or burned to a disc - and that requires the MKV format. With a $3 player program .mkv will play on an iPad, streaming ...

Initially, Handbrake became popular with the Mac OS ... It is one of the smoothest free MKV to MP4 converters. You can convert any video format of the video file to MP4 format.