Why did theodore roosevelt send the "great white fleet" on a world tour between 1907 and 1909? to avenge the surprise russian attack on u. s. forces in manila bay to conquer new colonial territories for the united states to defeat the boxer rebellion in peking to fight the japanese effort to conquer the philippines to demonstrate that the united states had arrived as a world power?

The best answer is, to demonstrate that the United States had arrived as a world power. 

President Theodore Roosevelt used the Great White Fleet as a means of show and status for the United States to its outside allies and adversaries. Without having to engage in warfare President Roosevelt demonstrated the naval power of the United States, which was especially important in the tumultuous international system of the early 20th century.