I am try to find out how the Unite States has shown its imperilistic nature?

I didn't know it had one. At least not like the old euorpean imperialistic regimes. That would infer that it had some sophistication, which it doesn't.

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Well you could consider the early idea of manifest destiny a type of imperialism. Also the U.S. acquisition of Alaska, Wake Island, Guam, the Philpiines, Cuba, and Puerto Rico. Other than manifest destiny during the 1800s, the U.S. hasn't really been about acquiring new land (even though we gained the other mentions territories) after that time. Usually if the U.S. took over a territory or occupied a territory, they quickly gave it its independence as soon as the country was stable enough to stand on its own.

Reading and studying information on sites of the following searches would also be helpful.

United States Demonstrating Imperialistic Tendencies - Google Search

America's Imperialistic Nature - Google Search