1. the spectra of star m is compared to a reference hydrogen spectrum. what can be concluded about star m? select all that apply.

(picture below it's the first one! )

star m is showing radial motion
star m is moving toward the earth
star m is moving away from the earth
star m is not showing radial motion, but it may have transverse motion
2. the blackbody curve for a star named theta is shown below. the most intense radiation for this star occurs in what spectral band?

(picture below it's the second one! )

ultraviolet light
visible light
infrared radiation
radio waves
3. select all that apply.

the following diagram shows the path a planet around the sun. kepler discovered that

(picture below it's the third one! )

the distance from p3 to p4 is the same as the distance from p4 to p5
the speed from p3 to p4 is the same as the speed from p4 to p5
the area of b equals the area of c
the area of b does not equal the area of c

1. The spectrUM of Star M is compared to a reference hydrogen spectrum. 

Star M is not showing any radial radial motion.  That is, it's not moving
toward the Earth or away from the Earth.  If it were doing either of those
motions, the star's Hydrogen lines would be shifted toward longer wave-
lengths (moving way), or toward shorter wavelengths (moving toward).
So it's not showing radial motion, but it may have transverse motion,
since motion across our sightline doesn't shift the star's spectrum. 

2. The blackbody curve for a star named Theta is shown below.
The peak intensity of this star's radiated wavelength occurs at
roughly 100 to 150 nanometers.  That's certainly much shorter 
than visible light, much much shorter than infrared, and much 
much much shorter than radio.  So from the choices listed, the
only one that COULD be correct is ultraviolet.  But to be honest,
100-150 nanometers is so very short, I think it actually belongs
in the X-ray family.
What I really want to know about this star is:  How did astronomer's
discover that its name is Theta ?

3. Referring to the third diagram that you attached, which shows the
path of a planet around the Sun:

--  the distance from P3 to P4 is obviously shorter than the distance
from P4 to P5, because P4-P5 is generally closer to the sun;

-- the speed from P3 to P4 is obviously less than the speed from
P4 to P5, because the diagram says that planet covers both arcs
in the same amount of time (t).

-- Kepler discovered that the area of B equals the area of C .
The line from the sun to the planet "sweeps" over equal areas
in equal amounts of time.
When you think about it, this means that any object in orbit around
the sun moves faster when it's closer to the sun, and slower when 
it's farther away from the sun.

In conclusion, I would be remiss if I didn't pause to express my gratitude
for the bounty of 5 points with which I have been showered in return for
this answer.  Not only do I cherish each and every one of those points,
but the green crust and warm turgid water have also been a welcome
and satisfying treat. 

That would be kinetic energy