Hi there Peter!
It sounds like you are seeing some odd behavior on your iPad after updating to iOS 9.0.2. I would start by quitting all the running apps on the device:
Force an app to close in iOS
1. Press the Home button two times quickly. You'll see small previews of your recently used apps.
2. Swipe left to find the app you want to close.
3. Swipe up on the app's preview to close it.
When you have done that restart the device and test the issue again:
iOS: Turning off and on (restarting) and resetting
If the issue persists, backup your device to iTunes, then restore it as new and verify that it works.
How to erase your iOS device and then set it up as a new device or restore it from backups
If it does, then restore your backup to either verify it still works and the software just needed reinstalled, or isolate the issue to the backup file itself.
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