Emission lines in the spectrum of the Crab Nebula exhibit a Doppler shift, which indicates that gas in that part of the nebula closest to us is moving toward us at 1450 km/s. Assume that the expanding gas has been moving at the same speed since the original supernova explosion, observed in 1054 A. D., and calculate what diameter (in light years) we should observe the nebula to have today.

Asmall metal bar, whose initial temperature was 10° c, is dropped into a large container of boiling water. how long will it take the bar to reach 70° c if it is known that its temperature increases 2° during the first second? (the boiling temperature for water is 100° c. round your answer to one decimal place.) sec how long will it take the bar to reach 98° c? (round your answer to one decimal place.)

Estimate the schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (assume that the your weight is 50 kg)

Glass has a hardness that is in the middle of the hardness scale. what is the hardness of glass?