"the import android.support.v7.app cannot be resolved" after updated

If you have the error of "the import android.support.v7.app cannot be resolved" after Android SDK and ADT updated in Eclipse. Try to Clean all projects, include appcompat_... libs.

Project (on Eclipse menu) -> Clean... -> select Clean all projects... then OK.

ic_launcher cannot be resolved or is not a field

Sometimes you will face with error of "ic_launcher cannot be resolved or is not a field", one of the possible reason is import android.R incorrectly.

Note: Eclipse sometimes likes to add an import android.R statement at the top of your files that use resources, especially when you ask eclipse to sort or otherwise manage imports. This will cause your make to break. Look out for these erroneous import statements and delete them.
~ http://source.android.com/source/using-eclipse.html