If I was invisible, I would go to Iraq or Afghanistan and help the U.S troops in battle. The enemy would not be able to see me and I could go in and kill them or get important info from their base or headquarters. This would make me a hero has many lives could be saved and threats wouldn't be unknown to us and other countries.
Another heroic thing i would do is guide the firefighters .Wherever the Firefighters would go I would follow to help them with things that they cant do. If someone was trapped in a burning house fire I would be able to go right in, pick them up and walk out all unharmed. Same thing with the cops. If they all going after a criminal, I would be able to stop them and the cops would have them. This would make more people more safe, less injured, and save lives as not all firefighter actions and cop chases are fully successful. The invisibility cloak would change the world within the right hands of the right person.