[C++]This as default parameter
Why can templates only be implemented in the header file?
What is the number of invertible $n\times n$ matrices in $\operatorname{GL}_n(F)$? $F$ is a finite field of order $q$. What is the size of $\operatorname{GL}_n(F)$ ?  I am reading Dummit and Foote "Abstract Algebra".  The following formula is given:  $(q^n - 1)(q^n - q)\cdots(q^n - q^{n-1})$.  The case for $n = 1$ is trivial.  I understand that for $n = 2$  the first row of the matrix can be any ordered pair of field elements except for $0,0$. and the second row can be any ordered pair of field elements that is not a multiple of the first row.  So for $n = 2$  there are $(q^n - 1)(q^n - q)$ invertible matrices.  For $n\geq 3$, I cannot seem to understand why  the formula works.  I have looked at Sloane's OEIS A002884.  I have also constructed and stared at a list of all $168$ $3\times 3$ invertible matrices over $GF(2)$.  I would most appreciate a concrete and detailed explanation of how say $(2^3 - 1)(2^3 - 2)(2^3 - 2^2)$ counts these $168$ matrices. Do you have to take the second leg of a domestic flight? A particle experiences an acceleration described by  $$ a=kx^{-2} $$ where x is the displacement from the origin and k is an arbitrary constant.  To what value does the velocity v of the particle converge to as x approaches infinity if the particle starts at some point x0?  If I approach this problem with energy, then $$ W = \int F \mathrm{d}x $$ $$  = \int_{x_0}^\infty mkx^{-2} \mathrm{d}x $$ $$  = mk(-\infty^{-1}+{x_0}^{-1}) $$ $$ W = K = mk{x_0}^{-1} $$ $$ \frac{1}{2}mv^2 = mk{x_0}^{-1} $$ $$ v = \sqrt{2k{x_0}^{-1}} $$  How would I solve this problem with pure kinematics? (there appears to be some sort of cyclical dependency where acceleration affects velocity, velocity affects displacement, and displacement affects acceleration)  Likewise, two particles experience accelerations described by $$ a_1=k_1x^{-2} $$ $$and $$ $$ a_2=-k_2x^{-2} $$ where x is the distance between the two particles  What two velocities do the particles reach as x approaches infinity if the two particles are initially separated by some x0? How do I evaluate several n-th derivatives of a function at one point? How to calculate the number of days you can stay in Taiwan on a tourist visa? Tourist visas to Taiwan have an associated "maximum stay" of 30 days. For those visas, how are the days counted? Does the stay begin on the partial day that the traveler arrives or the first full day spent in the country? Does it end on the last full day spent in the country, or the actual day the traveler departs? how can i display the latest items from another site collection I have a web application, with three site collections . and i want inside my team site to be able to display the latest pages that  have been added to my enterprise wiki site collection. so what are the available approaches which i can follow?  Thanks in advance for any help.  Regards Clipping a GEE Image with Python API I am looking for a way to clip image collection by a given polygon geometry with Python API, The GEE JavaScript equivalent is simply ImageCollection.clip(geom) () With the python API I get the error: 'ImageCollection' object has no attribute 'clip'.  I'm adding my code after using .mean() as a reducer My code: set the boundary polygon my_boundary = ee.Geometry.Polygon([ [[-5, 40],[65, 40],[65, 60],[-5, 60],[-5, 60]]] ,proj=None) #set the ImageCollection and Image img_Collection = ee.ImageCollection('COPERNICUS/S5P/NRTI/L3_NO2').filterDate('2020-03-01', '2020-03-27').select('NO2_column_number_density') my_Image=img_Collection.mean().clip(my_boundary) #Create Ipyleaflet map my_map = ipyleaflet.Map(zoom=7) my_map.add_layer(layer=my_Image) my_map error: AttributeError: 'Image' object has no attribute 'model_id' Book about classical mechanics I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical consideration related to these to formalism (like tangent bundle, cotangent bundle, 1-form, 2-form, etc.).  I have , but I would like to go into more details about the [symplectic] geometrical and mathematical foundations of classical mechanics.  Additional note: A chapter about relativistic Hamiltonian dynamics would be a good thing. I've been having a lot of problems trying to figure out how to use scanf().  It seems to work fine with integers, being fairly straight forward scanf("%d", &amp;i).  Where I am running into issues is using scanf() in loops trying to read input.  For example:  do {   printf("counter: %d: ", counter);   scanf("%c %c%d", &amp;command, &amp;prefix, &amp;input); } while (command != 'q');    When I enter in a validly structured input like c P101, it seems to loop again before prompting me.  This seems to happen even with a single:  scanf("%c", &amp;c)    in a while loop.  It'll do the loop twice before prompting me again.  What is making it loop twice, and how do I stop it? When I enter in less amount of input that programmatically wouldn't have another character or number such as q, pressing enter seems to prompt me to enter more.  How do I get scanf() to process both single and double character entries? It is written everywhere that gravity is curvature of spacetime caused by the mass of the objects or something to the same effect. This raises a question with me: why isn't spacetime curved due to other forces or aspects of bodies?  Why isn't it that there are curvatures related to the charge of a body or the spin of particles or any other characteristics? Why is observing 100 heads for a fair coin flips surprising? Assume that we have a fair coin. We flip it 100 times. The outcome is all heads. Why is it surprising? Doesn't all outcomes have the same probability? Any particular outcome, including irregular ones, would have the same very small probability. Why is it that observing an irregular outcome is less surprising to us than a regular one? Need to get logfile smaller Using Integration By Parts results in 0 = 1 How small a quantity should be added to x to avoid taking the log of zero? I have analysed my data as they are. Now I want to look at my analyses after taking the log of all variables. Many variables contain many zeros. Therefore I add a small quantity to avoid taking the log of zero.   So far I've added 10^-10, without any rationale really, just because I felt like adding a very small quantity would be advisable to minimize the effect of my arbitrarily chosen quantity. But some variables contain mostly zeros, and therefore when logged mostly -23.02. The range of the ranges of my variables is 1.33-8819.21, and the frequency of zeroes also varies dramatically. Therefore my personal choice of "small quantity" affects the variables very differently. It is clear now that 10^-10 is a completely unacceptable choice, as most of the variance in all the variables then comes from this arbitrary "small quantity".  I wonder what would be a more correct way of doing this.  Maybe it's better to derive the quantity from each variables individual distribution? Are there any guidelines about how big this "small quantity" should be?  My analyses are mostly simple cox models with each variable and age/sex as IVs. The variables are the concentrations of various blood lipids, with often considerable coefficients of variation.  Edit: Adding the smallest non-zero value of the variable seems practical for my data. But maybe there is a general solution?  Edit 2: As the zeros merely indicate concentrations below the detection limit, maybe setting them to (detection limit)/2 would be appropriate? What is the "continue" keyword and how does it work in Java? I saw this keyword for the first time and I was wondering if someone could explain to me what it does.   What is the continue keyword? How does it work? When is it used? What is a word for "cannot-be-wrong" attitude? When speaking with someone recently I was continuously taken aback by how he could not concede even the slightest detail in my argument (which was not unreasonable), and it happened another time previously. Both times had to do with me pointing out 'error' in his action.  He very much exhibits that 'I cannot be wrong' attitude.  I first thought to call this arrogance or pride but he is not overbearing like arrogance demands and he does not show excessive self esteem that pride demands.  What is a word that can accurately describe this attitude? What's the difference between iterating over a file with foreach or while in Perl? Cardioid in coffee mug? Template Hierarchy: confused with index.php, front-page.php, home.php I'm really confused with index.php, home.php and front-page.php. In many cases even though I had an index.php, I overwrite it with front-page.php. But recently, I became aware about home.php.   What's the difference between the home.php and index.php? What's the ideal condition to use a home.php than an index.php? What's the ideal condition to use a front-page.php? When I'm using a front-page.php then what specific task an index.php is doing for me then?   I've read the  in Codex. Please don't mix my question with Page Templates, I understand 'em, alHamduLILLAH. How to stop the find command after second match? How to make find command, that will show only first two matches and then end, something similiar to  just version for two records.