If M C R n is an orientable (n - 1)-dimensional manifold, show that there is an open set A C Rn and a differentiable g: A→ R1 so that M = g-1 (0) and g1 (x) has rank 1 for x ЄM.
Answer to relevant QuestionsLet M be an (n – 1) -dimensional manifold in Rn. Let M (Є) be the set of end-points of normal vectors (in both directions) of length Є and suppose Є is small enough so that M(Є) is also an (n- ...If w is a (k- 1) -form on a compact k-dimensional manifold M, prove that ∫Mdw =0. Give a counter-example if M is not compact.If Ί: Rn → Rn is a norm preserving linear transformation and M is a k-dimensional manifold in Rn, show that M has the same volume as Ί(M).A gas at 20°C may be rarefied if it contains less than 1012 molecules per mm3. If Avogadro’s number is 6.023E23 molecules per mole, what air pressure does this represent?The Stokes-Oseen formula  for drag on a sphere at low velocity V is: F = 3πμ DV + 9π/16pV2D2 Where D = sphere diameter, μ = viscosity, and ρ = density. Is the formula homogeneous?
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