PDOStatement::execute takes 11s, what to do?
It could mean any of a bunch of things.  PDOStatement::execute() is just the final method that gets called for each and every database query Drupal makes (which can be quite a few).

First, make sure you Apache is configured properly, and that APC is installed and has enough memory.

Then, I would make sure your MySQL instance has a decent starting point.  Download, run, and follow the advice of mysqltuner.

Then, download/install/enable the Performance Logging and Monitoring module and play around with the reports.

Figure out what is slow, and fix it.

There are also bunches of posts with other profiling advice, too, as well as advice for performance improvements beyond basic configuration (eg, advanced caching strategies).