The gladiator games were an example of what theory of rome's fall?

Which of the following arguments decided the debate over using the atomic bomb against japan in 1945? using the bomb would destroy the armaments still available to japanese forces in japan. using the bomb would demonstrate the power of the united states to the entire world. using the bomb would shorten the war and avoid heavy casualties among invading troops. using the bomb would enable allied forces to invade and take over the japanese mainland