The British had tons of internal and domestic problems to face their own, so basically from the beginning (early 1600's) they entered into a period of salutary neglect (where they didn't enforce their own laws)
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They became rivals because each one wanted more power than the other for example in world war 2 the USA made the atomic bomb which showed the world that the Americans were the most powerful country but after ww2 Russia and USA started a Cold War which lead to the feud between there political views and the start of better technology and the space race
I would say that’s true, this is not a department I’m strong in but I say true
Americans instituted an Open Door Policy both in China and Japan while Europeans insisted themselves by bringing addiction to the Chinese in the form of opium. Americans wanted to expand their trade and economy by creating the Open Door Policy for China to open their doors to the Americans. British people did not do this, they forced themselves into China which eventually led to their demise---the Opium Wars.