Please answer to all questions

Incorrect 0 / 1 pts Question 1 In polar coordinates the Cartesian area element dA=dx dy is replaced with an area of an elementary curvilinear rectangle given by O dA=r dr dtheta O dA=r theta dr dtheta O dA=dr dtheta O dA=r^2 dr dtheta Incorrect Question 2 0 / 1 pts A description of a surface in a three-dimensional space by parameterisation requires the introduction of O 2 parameters O 4 parameters O 3 parameters O 1 parameterIncorrect Question 3 0 / 1 pts Which of the following is not the purpose of surface parameterisation? O Effective "flattening" of a curved surface. O Enabling the reduction of a surface integral to a repeated integral over a rectangular region. O Enabling a straightforward choice of the integration limits. O Evaluating the length of the surface boundary. Incorrect Question 4 0 / 1 pts The area of a surface element is computed by evaluating O the sum of squares of the derivatives of the position vector with respect to parameters describing the surface O the product of magnitudes of the derivatives of the position vector with respect to parameters describing the surface the dot product of the derivatives of the position vector with respect to parameters describing the surface O the magnitude of the cross product of the derivatives of the position vector with respect to parameters describing the surfaceIncorrect Question 6 0 / 1 pts Normal vectors to a surface are found by O choosing one of the derivatives of the position vector with respect to parameters characterising the surface O computing a cross product between the derivatives of the position vector with respect to parameters characterising the surface O scaling the derivatives of the position vector with respect to parameters characterising the surface O computing a dot product between the derivatives of the position vector with respect to parameters characterising the surface Incorrect Question 7 0 / 1 pts The differential operator arising as a result of coordinate transformation in a plane is called O curl O Jacobian O gradient O LaplacianIncorrect Question 8 0 / 1 pts The flux integral involves O a normal component of a vector field to the integration surface the cross product of a vector field and the normal vector to the integration surface O a tangent component of a vector field to the integration surface O the magnitude of a vector field at the integration surface Incorrect Question 9 0 / 1 pts Stokes' theorem relates O cross and dot products surface integral and a line integral along an arbitrary path on this surface O curl and divergence O flux and circulationIncorrect Question 11 0 / 1 pts Green's theorem is O a clarification of Stokes' theorem O a generalisation of Stokes' theorem to multi-dimensional space O completely independent of Stokes' theorem O a particular case of Stokes's theorem applied to a flat surface Incorrect Question 12 0 / 1 pts If the curl of a vector field is zero everywhere, O so is its circulation along any closed path. then the work integral of this vector field can only be computed by parameterising the chosen integration path. O then the potential function cannot be introduced for this field. O then Green's theorem does not apply