1. One hectare, a unit of measure often used in measuring land areas, is defined to be 10 m2. In an effort to dig to China, a desperate grad student digs a pit 15 m deep over an area of 3 hectares before he happily dies of exhaustion. What volume of earth has he managed to exhume? Express your answer in: a) cubic meters, b) cubic kilometers, and c) gallons. 2. The fastest land animal is the cheetah, moving in bursts of speed up to 70 mph (miles per hour). The fastest fish in the sea, the sailfish swims at 30.5 m/s (meters per second). Which one is faster? Do your conversions by hand and show all your work. 3. An atom of oxygen has a mass of 16 u (atomic mass unit), and an atom of hydrogen has a mass of 1 u. a) What is the mass of a molecule of water (H2 O) in kg? b) The mass of water in the Earth's oceans is about 1.2x1021 kg. How many molecules of water make up this mass? 4. A can of paint claims to cover an area of 400 ft /gal. a) Express this quantity in square-meters per liter. b) Express this quantity in SI base units. c) Consider the inverse of the original quantity. What is the physical meaning of this new quantity? 5. A pendulum clock with a 12-hour dial happens to gain 2.0 minutes per day. After setting the clock to the correct time, how long will it take for the clock to read the exact correct time again? 6. Convert the following measurements to the units indicated: a) 34 nm - cm b) 0.0136 m/s um/min c) 9.3 m2 → mm? d) 98 cm-2→ km-2 e) 199 pF→ uF f) 66 ft-min./mg → m-s/kg 7. The unit of an acre-foot describes the volume of water that will cover 1 acre of land in a depth of 1 foot of water. Suppose a severe thunderstorm dumps 2.0 in. of rain on a town of area 26 km2. What volume of water, in acre-feet, fell on the town? 8. A fortnight is equal to two weeks (as in "fourteen nights"). How many microseconds are in a fortnight? 9. Grains of California beach sand are approximately spheres with a radius of, on average, 50 µm. They are made of silicon dioxide, which has a density of 2600 kg/m'. What mass of sand grains would have a total surface area (i.e. the total surface area of all the individual spheres) equal to the surface area of a cube 1.00 m on an edge? 10. A person on a diet might lose 2.3 kg per week. If this loss were uniform overt he course of the week, what would be the rate of weight loss in milligrams per second? 11. A traditional unit of length in Japan is the ken, where 1 ken=1.97 m. What are the ratios of: %3D a) square kens ot square meters, and b) cubic kens to cubic meters? What is the volume of a cylindrical water tank of height 5.50 kens and radius 3.00 kens in c) cubic kens, and