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Superconductors and hoverboards

We know that superconductors are repelled by magnetic fields. The earth has a magnetic field of about $10^{-5}$ Tesla. I just want to know if it is possible to use this property of earth to make ...
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Simple real life applications of Euler-Lagrange equations of motion

If you read some introductory mechanics text like David Morin's Introduction to Classical Mechanics about Euler Lagrange Equations you get a large amount of simple examples like the "moving plane" ...
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Will it ever be possible to observe the cosmic neutrino background?

Is there any foreseeable technology which would facilitate the direct observation of the cosmic neutrino background? Would the ability to warp spacetime have any application here?