Turning N over

A card with the letter N on it is rotated through two different axes. What does the card look like at the end?

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Problem



 

Image
Turning N Over

A square card printed with the letter N is held horizontally, as shown in the diagram, where the arrow indicates the direction of North.



The card is turned over by rotating it through $180^{\circ}$ about an axis running from East to West, and then turned over by rotating it through $180^{\circ}$ about an axis runnning from North-East to South West.

 

How does the diagram now look to a person facing North?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.