Export MOV to MP4 with Quicktime on Yosemite
If you have ffmpeg installed, it is quite easy to do it

ffmpeg -i input.mov output.mp4


If you don't, install it as follows:


Press Command + Space, type "Terminal" and press enter/return key.
Run this command in the Terminal app:

ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"


and press enter/return key.

If the screen prompts you to enter a password, enter your Mac's user password to continue. When you type the password, it won't be displayed on the screen, but the system would accept it. So just type your password and press ENTER/RETURN key. Then wait for the command to finish.
After that, run:

brew install ffmpeg

Done! You can now run ffmpeg -i input.mov output.mp4.


(For more information, you can refer to this site, or you can go directly to the official FFmpeg website: ffmpeg.org.)