The hot air inside a floating lantern has a density of 1.13 kg/m3. The
mass of the lantern is 0.154 kg. The
air outside the lantern is 1.29 kg/m3.
What is the buoyant force acting on
the floating lantern?
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Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1

This is important 1. what happens to the speed of molecules in water vapor when it condenses to form a liquid? (2 points) the molecules slow down. the molecules speed up. the molecules slow down and then speed up. the molecules speed up and then slow down. 2. how might human activities change to compensate for a decrease in water supplies? (2 points) humans might build a factory. humans might build drainage systems. humans might extract more water from the ground. human behavior does not change because of the water cycle. i'll be grateful if anyone can answer these 2 questions !

Two kilograms of air within a piston–cylinder assembly executes a carnot power cycle with maximum and minimum temperatures of 800 k and 300 k, respectively. the heat transfer to the air during the isothermal expansion is 60 kj. at the end of the isothermal expansion the volume is 0.4 m3. assume the ideal gas model for the air. determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kj.