(B) (5%) Let initial conditions be x₁(0) = x₂(0) = c1(0) =, and u(t) be the unit step function. Does the solutions of the differential equations converge to constant values as time approaches infinity? Justify your answers.

(b) (6%) Now set a = 1. Find functions g1and g2 such that {g1, g2} is an orthonormal set that satisfies Span(g1) = Span(f1) and Span(g1,g2) =Span(f1, f2).

(A) (4%) Find all possible values of β such that, the inverse of L, does not exist.

(b) (6%) Suppose that exists. Find the matrix representation of corresponding to the ordered base s{x+1，x - 1} and for P2 and R2, respectively. 

(A) (15%) Let u(t) ≡ 0 and the initial conditions be x1(0)=x2(0)=.Find the solutions of the differential equations.

15. (10%) Evaluate the following integral

1.1) According to the passage, what are the three factors that could be the reasons behind conficting research findings on the acquisition of grammatical morphemes? Explain your answer by summarizing the relevant paragraphs in your own words.

1.2) According to the passage, what are the three indications of a morphological congruency effect in the literature? Explain your answer by summarizing the relevant paragraphs in your own words. 

2.1) Imagine yourself as the researcher of this study. Based on the morphological congruency hypothesis, how do you predict the Russian and Japanese ESL speakers to perform on the self-paced reading task? Who will performn better and why? Also, in addition to the Japanese and Russian ESL speakers, is it necessary to include a group of English native speakers to test the hypothesis? Why or why not? Please be specific in explaining your answers. 

2.2) Think about your own foreign language learning/teaching experience. Does your experience support or refute the morphological congruency hypothesis? Do you agree or disagree with this hypothesis? Please provide some examples from your own observations in language leamning/teaching to support your position. 

1.翻譯:請將以下選文翻譯成準確順的中文·2.論述:a.使用語言:法文b.論述內容:细讀以下選文後·以原文的論远主題(sujet)為範園,由原文的論述內容(contenu)出發申論已見·切忌浮泛空洞流於個人感觸。長度至少應有300字,c.評分標準:文字正確和通暢與否估40%,述切题、條理清晰與否20%,見解兼具廣度與深度與否佔10%L'Etat est aujourd'hui incapable de prendre les mesures radicales qui s'imposent pourproteger les conditions d'habitabilite sur Terre et transformer profondement P'economie. [Lemode de pensee] de l'administration, bati apres-guerre pour accompagner la reconstructionpuis I'effort de modernisation, est en decalage complet avec la necessite actuelle, qui est defaire face a la mutation ecologique. L'Etat n'est donc pas en mesure de donner des directionsfiables a la population pour la proteger de cela. D'ailleurs, il ne dispose pas de I'autorite, etmeme de la legitimite d'imposer quoi que ce soit en ce sens. En matiere de protection de lasante, la societe civile a pris I'habitude depuis des siecles de s'en remettre a l'Etat, de lui faireconfiance. D'ou la docilite relative avec laquelle le confinement [sanitaire contre la Covid-19] a ete accepte. La situation est totalement differente dans le cas de la mutation ecologique.La sociste civile n'accepterait pas que l'Etat impose des gestes barrieres qui permettraient denous en proteger, qu'il restreigne les voyages en avion, stoppe la vente de pesticides, laisse lepetrole dans le sol... Peut-etre parce que la mutation ecologique a ete invisibilisee.                                                                                                                                   Bruno Latour,'"La crise sanitaire est une question de vie ou de mort, la mutation ecologique aussi"