This question has been asked before here but its answer is incorrect. I would like to rotate some views on screen orientation change, but I want to keep the layout unchanged
The basics are actually a lot easier. Have a look at Handling Runtime Changes.
First things first, by setting
android:configChanges="orientation|keyboardHidden|screenSize"
in your Manifest on your activity tag you can handle the orientation change yourself. (orientation should be enough, but there are sometimes issues where the event does not fire with that alone.)
You then skip onCreate and instead onConfigurationChanged gets called. Overwrite this method and apply your layout changes here. Whether you change your linearLayouts orientation here or have a custom view handling layout for different screens itself is up to you and depends on your implementation.
Animating will be a bit trickier, if it is even possilbe. A quick search says it is not.
Update for comment "I only want to rotate some views themselves rather than rotating the layout"
In theory it is possible to create your own layout and handle the drawing of your child views. I just tried it but could not produce any results in an appropriate time, but what you would need to do:
This is how I would do it.