Does the laws of gravitation apply to two energies as well?
Does everything with mass or energy have a gravitational pull?
Can anyone offer any help with this..? I read it at school around 1976 but cannot remember the title nor the author. Thank you in advance!  A lone astronaut called - I think- Steve is stranded on a distant planet when his ship runs low on fuel.   His only companion is - again I think - a parrot. The fuel his ship uses is a filament or wire which is kept on a spool.   On exploring the locale he has landed in he discovers a huge building half-buried in a mountainside. He enters the building and discovers it is a museum filled with thousands of glass cases containing preserved specimens of various life forms as well as machines.   There is a robot curator that does repairs and, as the astronaut finds out, prepares cases for new exhibits.   On analysing the wire in one of the machines he discovers that is suitable as fuel for his ship so he winds a length of it onto his ships spool and leaves the planet just ahead of the robot collecting him and his parrot as museum exhibits... Prove that the unit circle, $S^1:=\{(x,y)\in \mathbb{R}^2: x^2+y^2=1\}$, Is a one-dimensional manifold Which is more formal: "My parents will reside with me and my family" or "my family and I"? why does files (nautilus) open a new window although there's one already open? When I click on "files" in the launcher it opens another window although the normal action is to maximize the window already open. It doesn't always do that. Is it a bug? Using matplotlib in pygame $$A=\begin{array}{ccc} 0 &amp; 1/2 &amp; 0 &amp; \cdots &amp; 0 \\ 1/2 &amp; 0 &amp; 1/2 &amp;\cdots&amp; 0\\ 0 &amp; 1/2 &amp; 0 &amp; \cdots &amp; 0\\ \vdots &amp; \vdots &amp; \vdots &amp;\ddots &amp; 1/2\\ 0 &amp; 0 &amp; 0 &amp; 1/2 &amp; 0 \end{array}$$  I need to know the spectral radius of $A$ in function of the dimension of the matrix $n$. I know only one way to know the spectral radius, using the definition I find all eigenvalues and then find the maximum. but it very hard if $n$ is changing. Some help please!  I did some iteration by   $$det(\lambda I-A)$$  $$n=2 \quad r=\frac{\sqrt{1}}{2}$$ $$n=3 \quad r=\frac{\sqrt{2}}{2}$$  for $n=2$ and $n=3$ are correct.  and if we take this rule, for   $$n=5\quad \quad r=\frac{\sqrt{4}}{2}$$  but this isn´t true since I know radius for this matrix should be $&lt; 1$ and if we take this rule  for $n=5$ we have  $$\frac{\sqrt4}{2}=1$$   Some hint? I think I have managed to work this out, however there is no solution provided with the question so I thought it best to check.   My working:  Let $(x,y) \in (A \times B) \cup (C \times D)$  $\Rightarrow x \in (A$ or $C)$ and $y \in (B$ or $D)$  $\Rightarrow (x, y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow (A \times B) \cup (C \times D) \subseteq (A \cup C) \times (B \cup D)$  Now let $(x,y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow x \in (A$ or $C) $ and $y \in (B$ or $D)$  $\Rightarrow (x, y ) \in (A \times B) \cup (A \times D) \cup (C \times B) \cup (C \times D)$  $\Rightarrow (A \cup C) \times (B \cup D) \nsubseteq (A \times B) \cup (C \times D)$  $\Rightarrow (A \times B) \cup (C \times D) \not= (A \cup C) \times (B \cup D)$  Is this correct?  Thank you. How do I create a line graph which ignores zero values? I want to create a graph showing trends over time, calculated from a formula of various data.  However, some data is missing, resulting in zeroes in the calculated data which the chart uses.  When plotting this data against as a line graph, it's drawing a line down to the axis, which I don't want.  I'd like either a gap in the line, or skip the data point and draw from directly previous to next.  i.e. given this data:  00.0    61.6    39.5    74.6    86.8    72.0    66.5    99.5    85.6    80.6    95.0    122.4 81.0    83.1    88.2    00.0    94.3    60.5    00.0    99.5    95.8    86.2    00.0    111.4 84.1    110.8   78.9    62.0    75.9    102.2   89.9    87.1    81.6    73.5    00.0    116.9   All the 00.0 items mean "no data", so I'd like them ignored (not treated as 0 value).   This is the chart I currently have:   This is how I'd like the chart to come out:   Again, I don't mind if the dotted lines are blank or solid, so long as they don't go down to zero.  The data is dynamic/calculated, so I can't just say =AVERAGE(prev,next) since I don't know where missing data will occur in advance - I need a solution which takes this into account.  Any ideas? Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$ Need to find $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ Where $a_1\ge\dots\ge a_k\ge 0$  I thought about Cauchy Theorem on limit $\lim\limits_{n\to\infty}\dfrac{a_1+\dots+a_n}{n}=\lim a_n$ and something like what happen if all $a_i=0$ or $a_1=\dots=a_k$, but may be something I am thinking wrong?  Maybe it is too simple but I am not getting it; please help. Persistent Network Configuration using KVM and libvirt I've heard that you need to get a Mac if you want to develop iPhone apps. Is this true?   Is it possible to develop iPhone apps using Linux? If yes, what do I need and where do I download the necessary tools? combinatorics: sum of product of integer compositions When I cut a layer using marquee tool, I get blur edges to cut side. How do I get sharp edges after cut? I am using rectangular marquee tool to cut a portion of the layer in photoshop cs5, but after cutting, the edges are not sharp, I get blur edges.      how can I get sharp edges? Tiny navigation buttons and tags on responsive mobile I know it will be hard for you to tell on desktop because the resolution is so high, but the clickable text in the upper left, the icons on the upper right, and the navigation buttons at the bottom are all tiny. I have to squint to read the tags, I can't reasonably tap any navigation button except for Next without zooming, and selecting the achievements dialog, etc. is all very difficult. It seems to me that this would not be terribly difficult to change, so I am posting this feature request. I'm using a relatively large Samsung phone (Note 8), so I can imagine it would be worse on smaller phones.  Edit: I see from posted images that the responsive design on other phones looks nothing like mine. I'm wondering if it has something to do with the high resolution  where it thinks it is bigger than it is, or it's picking the wrong sizes because it's a tiny bit over some size threshold, in which case this would be a bug. What is the preferred way to mention Stack Overflow from Twitter? I wanted to tweet something on the lines of "Stack&nbsp;Overflow is awesome". When I do this kind of stuff, I usually use a username (for example: ) or a hashtag ()  I found , but it seems it is from someone unrelated with Stack&nbsp;Overflow.  Is there a Twitter account I can reference, or should I use a hash-tag? Should I just point to the site?  Thanks!  (Notice: I've seen lots of questions regarding Twitter and Stack&nbsp;Overflow, but those are mostly about integration/login with Twitter for the users accounts; I'm just asking for a single account for Stack&nbsp;Overflow; probably for announcements and PR, which is different) Who are the diamond moderators, and what is their role? Some people have a diamond after their username (e.g. )    What special privileges do diamond moderators have? How can I become a diamond moderator? Who are the diamond moderators?  How many are there?      For more information, see  in the .     Note: not to confuse with certain Stack Exchange employees, for example  members or "community managers", who often have diamonds as well, but are not ordinary moderators. How to determine the most likely reading frame of a DNA sequence? This question is from a past exam paper for an introductory bioinformatics module. I'm a computer scientist doing biology for the first time.  "A short bacterial gene has been sequenced, giving the following DNA sequence. Write out the 6 possible reading frames for this sequence and indicate which is the most likely protein translation of this sequence. Explain your reasoning for picking the given translation, and write all the translations in single letter amino acid code form.  5' - ttattcatccgccagcgccatgcgcgccat - 3'  "  I think I understand the 6 possible reading frames: three from the 5' end starting tta, tat and att; and three from the 3' end starting tac, acc and ccg.  I could also write out the translations for a given reading frame with a codon usage table. It's the most probable reading frame part I don't get. I thought perhaps I was looking for the longest open reading frame. I can only see one start codon (atg). What is the correct way to recognize the most probable reading frame?  I can't find this problem exactly on Biology Stack Exchange. I did find:     It made me wonder if I'm getting confused between "reading frame" and "open reading frame", this question only asks or the former.  Thanks! How does one install PlayOnLinux? How do I install PlayOnLinux on Ubuntu? When should I use a struct rather than a class in C#? When should you use struct and not class in C#? My conceptual model is that structs are used in times when the item is merely a collection of value types.  A way to logically hold them all together into a cohesive whole.  I came across these rules :   A struct should represent a single value. A struct should have a memory footprint less than 16 bytes. A struct should not be changed after creation.   Do these rules work? What does a struct mean semantically? Who is bound to the Prime Directive? In the galaxy there are a fair number of pre-warp societies. A Federation ship is not to contact them. But what about other, non-Federation species?   If for example a Ferengi ship passes by a pre-warp planet, would they be allowed to contact it? What would a Federation ship observing this contact have to do? Are they obliged to intervene? Are they allowed to? Or were they merely allowed to "strongly discourage" the attempt of the Ferengi?  If it is legal to use force to stop the Ferengi, than in essence the Ferengi were bound to the Prime Directive too. And if so: does this go for all Federation territory? Is this confined to the Federation territory? If Janeway observes such an incident, what are her rights to intervene? Or does she have the duty to do so?