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How to create a proper ortographic camera in libgdx

So I am having a little hard time understanding how ortographic cameras work in libgdx.
what I want is to have a camera that will only render things within a square while having another camera set the bounds for my whole screen.
So here, I was able to do what I wanted on the whole screen for the game pad. But, the thing you see on the top right is the background map of the game and i want to render the parts only fall within the red square you see here. How do I achieve that?
Are cameras supposed to do that or do I need to figure out a way to do it manually? I am really confused as to how cameras and projection matrices work.
Here on this screen, The red square and the green pad on the left are being drawn using the projection matrix of my screen camera. The map(top right) is drawn using my map cam.
Map cam is a view port of 400x400 but as you can see , the tiles are rectangular and that isnt the aspect ration i want. If someone can briefly explain how cameras work , I'd greatly appreciate it.
The reason I am not posting my code here is because I feel like I need to understand how camera mechanics work to even code it properly so I want to address that issue first.
Following #Tenfour04's advice worked perfectly. In case anyone wonders what I wanted to achieve. Here's a picture.

A camera alone cannot crop off part of the screen. For that you need to use glViewport. There is already a Viewport class in Libgdx that can do that for you. You will need two orthographic cameras (one for the map and one for the GUI), but the viewport can create its own.
private Viewport viewport;
//in create:
viewport = new FitViewport(400, 400);
//in resize:
viewport.update(width, height);
//in render:
viewport.getCamera().position.set(/*...move your map camera as needed*/);
viewport.apply(); //viewport cropped to your red square
batch.setProjectionMatrix(viewport.getCamera().combined);
batch.begin();
//draw map
batch.end();
//return to full screen viewport
Gdx.gl.glViewport(0, 0, Gdx.graphics.getWidth(), Gdx.graphics.getHeight());
batch.setProjectionMatrix(yourGUICamera.combined);
batch.begin();
//draw gui
batch.end();

What happens, is the camera will fit itself to the size of the screen. In order to change this, you would want to use a FrameBuffer. The frame buffer will constrain the camera into the desired size, then can be drawn as a texture.
Create the frame buffer with the dimensions being in pixels.
//Initialize the buffer
FrameBuffer fbo = new FrameBuffer(Format.RGB565, width, helght, false);
Render the world within the buffer.
fbo.begin();
//Draw the world here
fbo.end();
Draw the buffer to the screen with a batch.
batch.begin();
batch.draw(fbo.getColorBufferTexture(), x, y);
batch.end();

Rotating a Sprite in Java

While working on Projectiles I thought that it would be a good idea to rotate the sprite as well, to make it look nicer.
I am currently using a 1-Dimensional Array, and the sprite's width and height can and will vary, so it makes it a bit more difficult for me to figure out on how to do this correctly.
I will be honest and straight out say it: I have absolutely no idea on how to do this. There have been a few searches that I have done to try to find some stuff, and there were some things out there, but the best I found was this:
DreamInCode ~ Rotating a 1-dimensional Array of Pixels
This method works fine, but only for square Sprites. I would also like to apply this for non-square (rectangular) Sprites. How could I set it up so that rectangular sprites can be rotated?
Currently, I'm attempting to make a laser, and it would look much better if it didn't only go along a vertical or horizontal axis.

You need to recalculate the coordinate points of your image (take a look here). You've to do a matrix product of every point of your sprite (x, y) for the rotation matrix, to get the new point in the space x' and y'.
You can assume that the bottom left (or the bottom up, depends on your system coordinate orientation) of your sprite is at (x,y) = (0,0)
And you should recalculate the color too (because if you have a pure red pixel surrounded by blue pixel at (x,y)=(10,5) when you rotate it can move for example to (x, y)=(8.33, 7.1) that it's not a real pixel position because pixel haven't float coordinate. So the pixel at real position (x, y)=(8, 7) will be not anymore pure red, but a red with a small percentage of blue)... but one thing for time.

It's easier than you think: you only have to copy the original rectangular sprites centered into bigger square ones with transparent background. .png files have that option and I think you may use them.

Make a circle rotate around a point

Circle c1 = new Circle(20); //Initialize
c1.relocate(200, 200); //Set coordinates
I will say right off the bat that I do not understand trigonometry. From what I've been able to find online, I need to use cos and sin + an angle, but I do not understand how to make it happen.
How do I make the circle rotate around a specific point? I want to have a gap of 5-10 pixels between the rotation point and the circle's layout. So visually, the circle will be rotating around a blank space of 5-10 pixels.
Code snippets will be greatly appreciated, as well as tutorials.

How to get vertices of rotated Mesh in Libgdx without render?

First I would like to know if it's possible to rotate a Mesh without drawing it.
If it is possible then how could I get the new vertices of the rotated mesh?
I need this to verify if a certain Mesh is still inside a rectangle after rotation and, I only want to draw it if it still's inside.

Strange issues with texture mapping

I am attempting to use texture coordinates from a pre-generated PNG file on a 3d world of quads loaded into Java with LWJGL's slick-util extension.
The texture file is 192x96pixels, and properly formatted. It's composed of 6x3 32x32 tiles.
The 3d quads are 1.5f wide and long. They are spaced apart properly.
I am having issues getting the right texture coordinates. When I put 0.0f to 0.333333f as the y coordinates, I get slightly more than the top tile's height displayed. However, if I put 0.0f-0.25f, I get exactly 1/3rd, which is my tile's height. I have yet to find a magic number for the X coordinates, but maybe someone could explain to me why 1/4 of 96 is 24 according to textures coordinates, or what I'm doing wrong? I'm suspecting it could be a clash between my quad size and textures.
The tops of the cubes are using the texture coordinates (0.0, 0.0f), (0.0, 0.333333f), (0.166666f, 0.333333f), (0.166666f, 0.0f), which is applied moving anticlockwise from the top left to the top right. Again, the main texture file is 32x32 tiles arranged to make 192x96(96 is the height).
Notice I placed a white line at the top of one of the tiles to see its border, and black line at it's bottom, then a white line for the top of the next one below it. The texture 'bleeds' too far down. The other textures have their own even stranger coordinates, as you can see.
Arranging texture coordinates with the assumption the top of the image is 1.0 rather than the bottom produces odd squares with a rectangular hole in the center where quads should be.
I am using TEX_ENV GL_MODULATE.

Texture sizes are usually a power of 2. I suspect something resized your 192x96 texture as a 256x128 or 256x256 texture. This doesn't really explain the values you found however... But, I think, if you resize your texture to 256x256(increase the size, don't scale!) and calculate your texture coordinates based on that, your problem will go away.

I don't know about java but with my image atlases in objective C and openGL ES you need to make the textures smaller than what you are referring to when selecting them from the atlas.
Have you left a sufficient gap between the texture images to prevent 'bleeding?