Q:

What are these math symbols? 

I'm studying linear algebra and all of a sudden the symbol $\dot{+}$ appears. 
For example: 
$a*(v \dot{+} w) = a*v \dot{+} a*w$
Any idea what it might be?  
Also two more symbols.  they are on top of $0$ in equations: - and ~.
For example $u \dot{+} w = \bar{0}$ and
$\tilde{0}=\bar{0} + \tilde{0} = \bar{0}$.
Sorry if those questions are stupid but let's just say that linear algebra is not my favourite subject that I take in university 

A:

It seems that the first is a "decoration" of the usual symbol just used to highlight   the difference between this (abstract) operation in a vector-space and a "usual" addition in the real number say.  The context is not quite sufficient to be absolutely sure though. 
But one could have something like this: for $v,w\in V$ and $a,b \in \mathbb{R}$ one has $a(v \dot{+}w)= av \dot{+} a w$ and $(a+b)v = av \dot{+} bv$; note the usual plus, is in the real numbers the one with the dot in the vector-space.  
For the second it is more clear what is happening.  Every vector-space (or every additive group) has a "zero-element" that is an element that is neutral with respect to the additive operation.  One could also just denote this $0$ but one might use $\overline{0}$ to distinguish it from the $0$ in the real numbers.  
For example one can then say: for each $v \in V$ one has $0v= \overline{0}$; note the usual zero is the real number and we say that scalar multiplication by the real number $0$ yields the zero-element of the vectorspace.  
Finally the two different "decorations" are almost certainly part of a proof that the zero-element is unique.  So one assume there are two elements $\overline{0}$ and $\tilde{0}$ that behave like a zero-element and then shows they are equal.  
Summary: it is common to modify common symbols, like $+,0,1$ for keeping the intuition conveyed by the usual symbol while not using the exact same symbol for different things. 