Answer:
v = 24 cm and inverted image
Explanation:
Given that,
The focal length of the object, f = +8 cm
Object distance, u = -12 cm
We need to find the position &nature of the image. Let v be the image distance. Using lens formula to find it :

Put all the values,

So, the image distance from the lens is 24 cm.
Magnification,

The negative sign of magnification shows that the formed image is inverted.
Both the size and the shape of the tree changes
Answer: The amplitude is 0. (assuming that the amplitude ot both initial waves is the same)
Explanation:
When two monochromatic light waves of the same wavelength and same amplitude undergo destructive interference, means that the peak of one of the waves coincides with the trough of the other, so the waves "cancel" each other in that point in space.
Then if two light waves undergo destructive interference, the amplitude of the resultant wave in that particular point is 0.
So the equation for angular velocity is
Omega = 2(3.14)/T
Where T is the total period in which the cylinder completes one revolution.
In order to find T, the tangential velocity is
V = 2(3.14)r/T
When calculated, I got V = 3.14
When you enter that into the angular velocity equation, you should get 2m/s
Well dark matter is , in a layman terms just a concept used to identify missing mass in the universe. (extremely simplified and probably wrong but look that up). It could be but then if it is then we would still be able to percive the matter in some form. All we know from instruments is that they have mass and absorb light. We would need more info before any conclusions but it is 100% a possibility. But remember that when someone says "3-d" for example they are talking about a certain space.. technically matter exists on all planes (at least all the planes we know of in our local universe.) The laws of the cosmos are not yet proven to be constant and even if they are what of outside it?
When you take high school physics ask your teacher.