To examine and activate the terminal on the Vah Ruta water wheel, follow these detailed steps:

1. Ensure the Terminal is Upright:
– The terminal will not let you activate it if it’s upside down or tilted at an angle. Make sure it is standing right-side up.

2. Freeze the Water Wheel:
– The terminal inside the smaller, rotating gear is hidden because of a water spout. Use Cryonis on the spout to block it, but time it so that the terminal is upright. If it isn’t, you won’t be able to activate it.

3. Adjust Ruta’s Trunk Position:
– If the gear is not rotating, adjust Ruta’s trunk position using your map screen. Move the trunk so that water pours into the room, causing the gear to rotate.

4. Wait for the Orange Ball:
– Once the gear starts rotating, wait for the orange ball inside the gear to fall into the blue slot. This will ensure that the terminal is accessible.

5. Lock the Gear in Place:
– Use Stasis to lock the gear in place once the orange ball has fallen into the blue slot. This will keep the terminal upright and accessible for activation.

6. Activate the Terminal:
– Once the gear is locked in place, you should be able to examine and activate the terminal. If it still doesn’t work, ensure that there are no other obstructions or angles that might prevent activation.

By following these steps, you should be able to successfully examine and activate the terminal on the Vah Ruta water wheel.