I am looking for coordinates (longitude and latitude) of each state of Brazil. Where can I find that?  I have found a file for the US states here: , I am now looking for something similar for Brazil.
After learning about the  datasets I've working with the following layers, from the USA data   Country boundaries State boundaries County boundaries City boundaries ZipCode/Postcode boundaries   What I am trying to find is the equivalent (where appropriate) of the same data for various countries.  Is there any free administrative boundaries available as shapefiles for other countries?
Why do we use microwaves in microwave oven? We know that any object above absolute zero emits electromagnetic radiation. So hotter the object shorter the wavelengths. In the electromagnetic radiation spectrum radio waves has the longest then microwave, then infrared, then visible light, then ultraviolet, then x-ray, then gamma rays. Why do we use microwaves in microwave oven when infrared and visible light are much hotter and how do microwaves cook food when they are cooler than visible light and others. What happens if a target for removal becomes ineligible after a card has been cast? When you have a card like  which reads "Exile Target Creature with power 3 or less", as I understand it, it becomes untargetable if the opponent's creature power increases thanks to a pump spell like .  But what if the Disregard is already on the stack and targeting; and they respond with Brute Strength? I'm pretty sure (and my opponent with Brute Strength was certain) that it won't exile the creature, but I don't know which rule states this, and there's no gatherer ruling on the spell. I ask this Question on behalf of my neighbor.   Their 12 year old son saw his parents having sex.  As there is only one room in their home we can't say its the parents' mistake... but now the question is how do they handle the situation? Inverse of a Positive Definite Matrix Group induction proof and order of elements question $H$ is the set of the matrices $A$ of the form $$A= \begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}$$  where $0\leq \theta &lt; 2\pi$  is a group with respect to matrix multiplication.  Question part (1) Prove by induction that  for any $\theta$ and any positive integer $n$,  $$\begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}^{n} = \begin{pmatrix} \cos(n\theta) &amp; \sin (n\theta) \\ -\sin (n\theta) &amp; \cos (n\theta)\end{pmatrix}$$   When $n =1$ we have $$\begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}^{1} = \begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}$$   and clearly this holds for the base case.   Now I'm going to assume true when $n=k$ and try and prove for $k+1$. So we have   $$\begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}^{k}\begin{pmatrix} \cos(\theta) &amp; \sin (\theta) \\ -\sin (\theta) &amp; \cos (\theta)\end{pmatrix}^{1} = \begin{pmatrix} \cos(k\theta + \theta) &amp; \sin (k\theta + \theta) \\ -\sin (k\theta + \theta) &amp; \cos (k\theta + \theta)\end{pmatrix}$$   Now I'm sure I can cheese this, but is there some clever way to pull this apart? I want to just be able to say something like the determinant of the left side is $1^{k+1}$ and its the same on the right ...  Question part (2) Find an element of $H$ of order 5.  Here I'm totally lost, I seem to think that every element is of order 1 cause the determinant is 1.  Question part (3) Find an element of $H$ of infinite order.  Again I'm lost; I want to somehow make the determinant 0 for this but it can never be 0 for any $\theta$. How to test with Math.random in JavaScript? Export tikz as image file Which props in Star Trek: Picard are reused from the original TNG show and films (if any)? I am in doubt as to whether the subject-verb agreement of the second sentence of this paragraph is correct :  Unfortunately, there is no such thing as the ideal home workshop because most people are limited by the space available and by their budget. However, the information and diagram here acts as a guide to help you formulate a sensible workshop layout and a machinery “wish list”.  I suppose if the compound subject is seen as a single unit, then the sentence can be considered as correct. A little further in the same book, another sentence has a singular verb with a compound subject :  Alternatively commandeer a garage, or build yourself a substantial workshop if outdoor space and permission allows – however, do consider the impact of machinery noise on your neighbours.  Can &quot;outdoor space and permission&quot; be seen as one thing, or would this be considered a mistake ? Best way to obtain clarifying information when reputation doesn't allow comments? How can I change what keys on my keyboard do? (How can I create custom keyboard commands/shortcuts?) I have two tensors that i must calculate double dot product. matrix A is rank 2  and matrix B is rank 4. I want to multiply them with Matlab and I know in Matlab it becomes: A : B = trace (A*B) but it has one error and it says: Inner matrix dimensions must agree So how can I solve this problem? anybody help me? Thanks Shift + Control + Space doesn't seem to work anymore. Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime. Consider numbers of the type $n=2^m+1$. Prove that such an $n$ is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime. Consider numbers of the type $n=a^m-1$ where $a&gt;1$ is a natural number. Prove that such an $n$ is prime only if $n=M_p$ for p-prime, where $M_p$ is a Mersennt Prime.   I do not understand what the question is asking me for. Can I get some clarification? How to compile a function whose arguments are lists containing strings? Dropping the '-ing' in noun adjuncts I always remember many verbs ending in -ing.  Swimming club/cap and shaving foam for example. I now see increased use of swim club and shave foam.  Why has this happened, is it correct use of English ? Connect iPhone to Mac Without Charging I am developing iOS apps and I hate, that always when I connect my iPhone to my Mac to install and test an app, the iPhone gets charged. Is there any possibility to connect my iPhone to my Mac without charging the phone?    My Environment: -  iPhone 4S (No Jailbreak) -  MacBook Air3,2 (Late 2010) Should I use the past tense with did? For example, I was to say:     The important question is: Did they knew what it means or not?   Or should I say:     The important question is: Did they know what it means or not?   In other words: Should I use past tense with did?  I looked at this:    but it didn't really answer my question. Can we balance the whitespace above/below headings? In January, some additional whitespace  below h1, h2 and h3 headings,  more whitespace below the headers than above them.  Could we have the whitespace above the headings be more than the whitespace below them?  I find some posts a bit hard to read, like the current rendering on the left:   &nbsp; &nbsp; &nbsp; Maximum of $|\sin(z)|$ as $\{z: |z| \leq 1 \} $  So according to the Maximum Principle, the maximum is when $|z|=1$. I tried using the fact that $\sin z= \dfrac {e^{iz}-e^{-iz}}{2i}$, but didn't know how to continue from there. Setting $z=e^{it}$ doesn't help much.  I saw this question was answered before, however the answer uses hyperbolic functions ($\sinh, \cosh$) which I haven't actually studied.  Thanks in advance for any assistance!