C

9000123102

Level: 
C
Find a true statement about the ellipse x2+4y2−8y=0.
The tangent to the ellipse can pass through any point on the line y=−1.
The tangent to the ellipse can pass through any point on the line x=1.
The tangent to the ellipse can pass through the point [−1;1].
The tangent to the ellipse can pass through any point on the line y=1.

9000117703

Level: 
C
For an isothermal process in an ideal gas the product pV is constant (Boyle's law). In a pressure-volume diagram which shows p as a function of V this law describes a hyperbola (called isotherm). Do we have enough information to identify the asymptotes? If so, find these asymptotes.
p=0, V=0
p=V, p=−V
p=0, p=V
It is not possible to draw any conclusion.

9000117704

Level: 
C
Given physical quantities and laws relating these quantities, identify an answer where the graph which relates these quantities is a part of a hyperbola. (The other quantities are supposed to be constant.)
The pressure (p) and the area (S) over which the pressure is distributed, if F=p⋅S.
The mass (m) and the kinetic energy (Ek) of a moving body, if Ek=12⋅m⋅v2.
The velocity (v) and the kinetic energy (Ek) of a moving body, if Ek=12⋅m⋅v2.
The mass (m) and the potential energy (Ep) in a homogeneous gravitational field, if Ep=m⋅g⋅h.

9000117705

Level: 
C
Given physical quantities and laws relating these quantities, identify an answer where the graph which relates these quantities is a part of a parabola. (The other quantities are supposed to be constant.)
The electrical work (W) and the current (I), if W=R⋅I2⋅t.
The mass (m) and the acceleration (a) of a moving body, if F=m⋅a.
The height (h) and the potential energy (Ep), if Ep=m⋅g⋅h.
The electrical work (W) and the time (t), if W=R⋅I2⋅t.

9000117706

Level: 
C
Satellites travel along approximately circular paths. Consider a satellite in the height h measured from the Earth surface. Further, consider the coordinate system with origin on the Earth surface directly below the satellite and the y-axis oriented up (to the satellite). The x-axis is perpendicular to y-axis and it is in the plane defined by the trajectory of the satellite. Neglect the Earth's rotation and find the equation which describes the path of the satellite. The Earth radius is R.
x2+(y+R)2=(R+h)2
x2+y2=(R+h)2
x2+(y+R)2=h2
x2+y2=h2