Does the earth rotate with same speed in Australia as in The Netherlands?

Depends on what you mean by "rotate with [the] same speed".

All points on Earth rotate once a day. But if you're calculating the actual "speed" (that is, the tangential velocity, or the velocity with which an object would fly away from Earth if gravity suddenly switched off), that decreases as you move away from the equator. So any two points on Earth's surface have roughly the same tangential velocity as long as they have the same latitude.

(I say "roughly" because there is some minor variation by altitude, but it doesn't make a big difference.)

Let's talk about Australia first. The northernmost point in Australia is at Cape York, which is about 10º41' south latitude. The southernmost point in the Australian mainland is called, appropriately enough, South Point, which is at 39º08' south latitude. If you include the island of Tasmania, then Australia's southernmost point is at South East Cape (43º39' south latitude).

The northernmost and southernmost points in the Netherlands are, respectively:

Rottumerplatt (53º33' N)
Boundary marker 12 (50º45' N)

As you can see, the Netherlands is (are?) further north than Australia is south, ergo, everybody in Australia is physically moving faster than anybody in the Netherlands. However...both countries still experience 24-hour days.

I hope that helps. Good luck!

The Earth rotates once every 24 hours everywhere, because it is a solid body. But the actual velocity varies with latitude. Think of the difference between someone standing at one of the poles, moving very slowly, with somebody standing on the equator, moving much faster because they are farther from the axis of rotation.

The Netherlands is at latitude 52°N while Australia is at latitude 35°S. so the Netherlands is closer to the polar axis, and moves more slowly than Australia, which is closer to the equator and farther from the axis.

All of the Australian continent including Tasmania has the same angular velocity as all other places on the Earth.

A disk rotates at a speed of r.p.m. (revolutions per minute). So the speed of rotation is the same all over the disk. But the linear speed near the center of the disk is much slower than that at the circumference of the disk (for example, inches per minute). An ant in the middle of the disk would not be pulled away by the centrifugal force, whereas one on the edge of the disk would. So your answer depends on what you mean by speed here: r.p.m. or linear.
R.p.m. = speed is the same
Linear speed = not the same

The Earth is a fairly rigid body, it rotates once a day everywhere.

The Earth travels at the same speed in different parts of it.

Depends on how you look at it... Yes, they both circle the Earth's axis once per day; or, you can calculate their surface speeds by what latitude they occupy - the closer to the equator you are, the faster you *move* around the axis to complete the trip in 24 hours.

A location with latitude A travels a distance 2*pi*R *cos A miles in 24 hours, where R is the radius of the earth.
For Adelaide, A is about 35 degrees: for Amsterdam, it's about 52 degrees.
So an observer on the moon, say, would see those two points moving at different speeds.

One rev per day no matter where you are.

No, they are not equidistant from the equator. The Earth can be treated as a rigid body when it rotates for the purpose of this question. If you stood on the north or south pole you don't go anywhere just spin while standing still. If you stand on the equator you're moving at about 1000 miles per hour. Traveling the entire circumference of the Earth in one day. That is because the circle you describe has the widest diameter at the equator and gets smaller the closer you are to the poles, yet everyone completes the journey (big or small) in the same time (24 hours).

This means that in terms of degrees per minute everyone rotates at the same speed also in terms of revolutions per minute we all travel at the same speed but in terms of miles or kilometres per hour we're travelling at different speeds.