In 1898 the united states annexed hawaii. which scenario best describes what the word 'annexed' means? a) hawaii officially became the 50th state in the united states. b) hawaii became fully controlled by the united states and lost all self-autonomy. c) hawaii became a "favorite nations" ally of the united states and would be protected if attacked. d) hawaii became a protectorate of the united states, and could control their own local economy, while the united states controlled hawaii's international economy.

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randy pausch was a famous mathematician, writer and lecturer who is particularly famous for his last speech, given in 2007, "the las lecture", because he illustrates why one's dreams need to be pursued in a logical order if success is to be obtained, option c. at this time, pausch had been diagnosed with terminal cancer so he told the audience to follow their childhood dreams, which were possible to achieve. it has been recognized as one of the best motivational speech around the world.

the revival of interest in greek and roman influences also stimulated developments in math and science. the mathematical traditions that governed the conception of the universe were based in greek mathematics that had been preserved and built upon by scientists in muslim lands, such as nasir al-din in the 13th century. the catholic church endorsed the views of ptolemy, the greek philosopher and astronomer who constructed a geocentric theory where all planets, the moon, and the sun revolved around the earth. using calculations from al-din, polish monk and mathematician, nicholas copernicus, concluded that the geocentric theory did not make sense. instead, his data indicated that the earth and all the other planets rotated around the sun, a conclusion that he did not share widely, for fear of retaliation from the church. in fact, his heliocentric theory was not published until after his death in 1543.

the scientist that really got into trouble over the heliocentric theory was italian galileo galilei, who strengthened and improved copernicus' theory. other scientists, such as johannes kepler, had demonstrated that planets also moved in elliptical orbits, and galileo confirmed those theories as well. perhaps most famously, he built a telescope that allowed him to observe the phenomena directly, recording details of heavenly bodies that the ancients could never have known about. galileo's theories were published in the starry messenger in 1610, a highly controversial book criticized by other scientists, as well as officials of the church. galileo made the mistake of making fun of people that disagreed with him, and he was arrested and put on trial, eventually recanting his theory publicly in order to save his own life.